Question

The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle.

Answer 1

Let the base and height of right triangle is x and y respectively

Given: hypotenuse = 17 cm

So, $x+y+17=40cmx+y=23cmx=23-y.......\left(1\right)and{x}^2+y^2=z^2......\left(2\right)\Rightarrow (23-y{)}^2+y^2={17}^2\Rightarrow 529-46y+y^2+y^2=289\Rightarrow 2y^2-46y+240=0\Rightarrow y^2-23y+120=0\Rightarrow (y-8\left)\right(y-15)=0\Rightarrow y=15or8\Rightarrow x=8or15,So,Area=\frac{1}{2}\times b\times h=\frac{1}{2}\times 8\times 15=60c{m}^2$