Question:
A piece of paper is in the shape of a right-angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?
A piece of paper is in the shape of a right-angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?
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In problems involving scaling, use the square of the scaling factor to calculate changes in area.
Updated On: Aug 1, 2025
- 16.665
- 16.565
- 15.465
- 14.365
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The Correct Option is A
Solution and Explanation
We are given that the hypotenuse was reduced by 35%, so the scale factor for the smaller triangle is $1 - 0.35 = 0.65$. The area of a triangle scales with the square of the scale factor, so the area of the smaller triangle is:
\[
\text{Area of smaller triangle} = 34 \times (0.65)^2 = 16.665
\]
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