Quantitative Aptitude

Geometry

1,950 Questions
All Circle Tangents and Chords 772 Coordinate Geometry 360 Circle and Arc Measures 216 Triangle Centers and Medians 175 Composite and Inscribed Shapes 174 Similarity, Congruence, and Proportionality 118 Right Triangles and Pythagorean Theorem 100 Standard 2D Mensuration 22 Polygon and Angle Sums 10 3D Solid Mensuration 3

Geometry Questions

Multiple choice

Two triangles have corresponding sides of 7 cm, 24 cm, and 25 cm, and 14 cm, 48 cm, and 50 cm respectively. Are the triangles similar?

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To determine if the triangles are similar, we need to check if the ratios of their corresponding sides are equal. The ratios are 7/14 = 1/2, 24/48 = 1/2, and 25/50 = 1/2. Since all the ratios are equal, the triangles are similar.

Multiple choice

In a triangle ABC, the side AB is 10 cm and the side AC is 12 cm. If the triangle is similar to triangle DEF, where DE is 15 cm, what is the length of DF?

  1. 18 cm

  2. 20 cm

  3. 22 cm

  4. 24 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/DE = AC/DF. Substituting the given values, we get 10/15 = 12/DF. Solving for DF, we get DF = 20 cm.

Multiple choice

Two triangles have corresponding sides of 9 cm, 15 cm, and 20 cm, and 18 cm, 30 cm, and 40 cm respectively. Are the triangles similar?

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To determine if the triangles are similar, we need to check if the ratios of their corresponding sides are equal. The ratios are 9/18 = 1/2, 15/30 = 1/2, and 20/40 = 1/2. Since all the ratios are equal, the triangles are similar.

Multiple choice

In a right triangle ABC, the hypotenuse AB is 40 cm and the side AC is 24 cm. If triangle PQR is similar to triangle ABC, where PQ is 60 cm, what is the length of QR?

  1. 36 cm

  2. 48 cm

  3. 60 cm

  4. 72 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 40/60 = 24/QR. Solving for QR, we get QR = 48 cm.

Multiple choice

A right triangle has a hypotenuse of 10 inches and one leg of 6 inches. What is the length of the other leg?

  1. 4 inches

  2. 6 inches

  3. 8 inches

  4. 10 inches
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs. In this case, the hypotenuse is 10 inches and one leg is 6 inches. So, the other leg is √(10^2 - 6^2) = √(100 - 36) = √64 = 8 inches.

Multiple choice

In a right triangle, if the angle opposite the hypotenuse is 30 degrees, then the ratio of the length of the opposite side to the length of the hypotenuse is:

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a 30-60-90 triangle, the ratio of the length of the opposite side to the length of the hypotenuse is 1/2.

Multiple choice

In a right triangle, if the angle opposite the hypotenuse is 60 degrees, then the ratio of the length of the opposite side to the length of the hypotenuse is:

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

In a 30-60-90 triangle, the ratio of the length of the opposite side to the length of the hypotenuse is sqrt(3)/2.

Multiple choice

If the length of the hypotenuse of a right triangle is 10 cm and the length of the adjacent side is 6 cm, what is the length of the opposite side?

  1. 8 cm

  2. 4 cm

  3. 12 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $6^2 + b^2 = 10^2$. Solving for $b$, we get $b = 8$ cm.

Multiple choice

In a right triangle, if the length of the hypotenuse is 13 cm and the length of the opposite side is 5 cm, what is the length of the adjacent side?

  1. 12 cm

  2. 6 cm

  3. 10 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 5^2 = 13^2$. Solving for $a$, we get $a = 12$ cm.

Multiple choice

A right triangle has an adjacent side of length 8 cm and an opposite side of length 6 cm. What is the length of the hypotenuse?

  1. 10 cm

  2. 14 cm

  3. 12 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $8^2 + 6^2 = c^2$. Solving for $c$, we get $c = 10$ cm.

Multiple choice

If the hypotenuse of a right triangle is 20 cm and the opposite side is 12 cm, what is the length of the adjacent side?

  1. 16 cm

  2. 8 cm

  3. 14 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 12^2 = 20^2$. Solving for $a$, we get $a = 16$ cm.

Multiple choice

In a right triangle, if the length of the hypotenuse is 17 cm and the length of the adjacent side is 8 cm, what is the length of the opposite side?

  1. 15 cm

  2. 12 cm

  3. 10 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $8^2 + b^2 = 17^2$. Solving for $b$, we get $b = 15$ cm.

Multiple choice

If the opposite side of a right triangle is 7 cm and the hypotenuse is 13 cm, what is the length of the adjacent side?

  1. 12 cm

  2. 8 cm

  3. 10 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 7^2 = 13^2$. Solving for $a$, we get $a = 12$ cm.

Multiple choice

In a right triangle, if the length of the hypotenuse is 25 cm and the length of the opposite side is 20 cm, what is the length of the adjacent side?

  1. 15 cm

  2. 10 cm

  3. 12 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 20^2 = 25^2$. Solving for $a$, we get $a = 15$ cm.

Multiple choice

If the legs of a right triangle are 3 cm and 4 cm, what is the length of the hypotenuse?

  1. 5 cm

  2. 7 cm

  3. 12 cm

  4. 16 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have: (a^2 + b^2 = c^2). Substituting the values, we get: (3^2 + 4^2 = c^2). Simplifying, we get: (9 + 16 = c^2). Therefore, (c^2 = 25) and (c = 5).