Question

The long leg of a right triangle is 71 feet longer than the short leg.The hypotenuse is 85 feet long, how long are the legs of the right triangle?

Answer 1

Given

The hypotenuse is given 85 feet long.

The long leg of a right triangle is 71 feet longer than the short leg.

Explanation

Let the longer leg be x and short leg be y.

Then the relation obtained is

`x=71+y`

Then the figure obtained is

Now apply the Pythagoras theorem,

`\begin{gathered} 85^2=x^2+y^2 \\ 85^2=(y+71)^2+y^2 \\ 7225=y^2+5041+142y+y^2 \\ 7225-5041=142y+2y^2 \\ 2184=142y+2y^2 \\ 2y^2+142y-2184=0 \\ (y-13)(y+84)=0 \\ y=13,-84 \end{gathered}`

The value of y cannot be negative,hence the value of y obtained is 13.

Now find the value of x.

`\begin{gathered} x=71+y \\ x=71+13 \\ x=84 \end{gathered}`

Answer

Hence the length of shorter leg is 13 feet.

The length of longer leg is 84 feet.