A field in the shape of a right triangle has an area of 30square meters. If one leg of the right triangle thatforms the field is 4 meters longer than the other leg,what is the length of the longer leg?
Accepted Solution
A:
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 + 4The area of triangle is given as,[tex]\text { area of right triangle }=\frac{1}{2} \times 1 \text { st leg length } \times \text { 2nd leg length }[/tex][tex]\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}[/tex]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.