Question

A field in the shape of a right triangle has an area of 30
square meters. If one leg of the right triangle that
forms the field is 4 meters longer than the other leg,
what is the length of the longer leg?​

Answer 1

The length of longer leg is 10 meters.

Solution:

Given, A field in the shape of a right triangle has an area of 30 square meters.  One leg of the right triangle that forms the field is 4 meters longer than the other leg,  

We have to find what is the length of the longer leg?

Let the length of one 1st leg be b, then length of 2nd leg will be b + 4

The area of triangle is given as,

$\text { area of right triangle }=\frac{1}{2} \times 1 \text { st leg length } \times \text { 2nd leg length }$

$\begin{array}{l}{30=\frac{1}{2} \times b \times (b+4)} \\\\ {2 \times 30=b \times (b+4)} \\\\ {2 \times 3 \times 10=b \times (b+4)} \\\\ {6 \times 10=b \times (b+4)} \\\\ {6 \times(6+4)=b \times (b+4)}\end{array}$

So, by comparison b = 6 , then lengths of two legs will be 6, 6+4 = 10.

Hence, the length of longer leg is 10 meters.