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) 16.665 

(b) 16.565 

(c) 15.465 

(d) 14.365

Answer 1

(d) 14.365

Given, ST || RQ

∴ \(\frac{\text{Area of ΔSPT}}{\text{Area of ΔRPQ}}\) = \(\frac{ST^2}{RQ^2}\)

Also, given ST = \(\bigg(1-\frac{35}{100}\bigg)RQ\) = (0.65) RQ

∴ \(\frac{ST}{RQ}\) = 0.65 ⇒ \(\bigg(\frac{ST}{RQ}\bigg)^2\) = 0.4225

⇒ \(\frac{\text{Area of ΔSPT}}{\text{Area of ΔRPQ}}\) = 0.4225 ⇒ \(\frac{\text{Area of ΔSPT}}{{34}}\) = 0.4225

⇒ Area of ΔSPT = 0.4225 x 34 = 14.365