Multiple choice

Find the area (in sq. units) of the circle inscribed inside the triangle formed by the lines 5π‘₯ + 12𝑦 βˆ’ 60 = 0 and the coordinate axes.

  1. 4Ο€

  2. 6.25Ο€

  3. 9Ο€

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

The line 5x + 12y = 60 intersects axes at (12, 0) and (0, 5). This is a right triangle with sides 5, 12, 13. The inradius r = (a+b-c)/2 = (5+12-13)/2 = 2. Area of circle = pi*r^2 = 4pi.

AI explanation

The line 5x plus 12y minus 60 equals 0 forms a right triangle with the coordinate axes. The intercepts are x equals 12 and y equals 5, making the hypotenuse 13 units long by the Pythagorean theorem. The radius of the incircle of a right triangle is given by the formula (a + b - c) divided by 2, where a and b are the legs and c is the hypotenuse. Thus, the inradius is (5 + 12 - 13) divided by 2, which equals 2. The area of the inscribed circle is pi times r squared, resulting in 4 pi square units.

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