Multiple choice

In a right triangle, one angle is 45°. If the hypotenuse is 10√2 cm, what is the length of each equal side?

  1. 8 cm

  2. 10 cm

  3. 12 cm

  4. 14 cm
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B Correct answer
Explanation

In a 45-45-90 triangle, the sides are in ratio 1:1:sqrt(2). Given hypotenuse = 10*sqrt(2), the legs are 10 cm each.

AI explanation

Since the right triangle has one angle of 45 degrees, it is an isosceles right triangle where the two perpendicular sides are equal. Let the equal sides be x, so by the Pythagorean theorem, x squared plus x squared equals the hypotenuse squared, giving 2x^2 = (10 times the square root of 2)^2. This simplifies to 2x^2 = 200, meaning x^2 = 100. Taking the positive square root, x is 10 cm. The result is 10 cm.

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