Question

If a piece of paper is in the shape of right angled triangle and is cut along the 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 original
triangle was 34 sq inches, before the cut.What is the area of smaller triangle ?

Answer 1

Given:

There was 35% reduction in the length of the hypotenuse of the triangle,

Therefore the length and breadth of the smaller triangles will be 0.65b and 0.65h respectively.

Then, $Ratio\ of\ larger\ to\ smaller\ triangle=\frac{Area\ of\ original\ triangle}{Area\ of\ smaller\ triangle}$

$=\frac{\frac 12*b*h}{\frac 12*0.65b*0.65h}=\frac{1}{0.65^2}=(\frac{20}{13})^2$

By substituting we get the area of smaller triangle as  

$34*\frac{169}{400} = 14.365 sq. inches$.

Smaller triangle will be similar to the larger triangle and each side will have same ratio as compared to the corresponding side of the larger triangle.