Question

The hypotenuse of a grassy land in the shape of a right triangle is $1$ meter more than twice the shortest side. If the third side is $7$ meters more than the shortest side, find the sides of the grassy land.

• A. $8,15$ and $17$
• B. $7,14$ and $15$
• C. $6,13$ and $13$
• D. $5,12$ and $11$

Answer 1

Answer: (A)

$8,15$ and $17$

Let the shortest side be $x$

Given the hypotenuse $=1+2x$

And third side $=7+x$

$\Rightarrow x^2+(7+x{)}^2=(1+2x{)}^2$

$\Rightarrow 2x^2+14x+49=4x^2+4x+1$

$\Rightarrow x^2-5x-24=0$

$\Rightarrow (x-8)(x+3)=0$

$\Rightarrow x=8,-3$

As the side is always positive $\Rightarrow x=8$

$\therefore$ Sides are $8,15,17$