Question

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

Answer 1

Let the length of the shortest side be x metres.

Then,

Hypotenuse = (2x+1) metres

Third side = (x+7) metres

By pythagoras theorem,

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

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

$2x^2-10x-48=0$

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

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

$x=8,-3$

$x=8$ $[x\ne -3]$

Hence, the lengths of the sides of the grassy land are 8 metres, 17 metres and 15 metres.