## Judy planted vegetables on a piece of land. The land is in the right-angled triangular shape. Given the longest side of the land is y metre.

Question

Judy planted vegetables on a piece of land. The land is in the right-angled triangular shape. Given the longest side of the land is y metre. The other two sides of the land are 2x metre and (2x+6) metre respectively. He fenced the land with 72 metres of barbed wire. Find the length, in metre , of each side of the land.

## Answers ( No )

We know that the perimeter is 72 meters, so we have

Now we can use the pythagorean theorem: the sum of the squares of the legs is the square of the hypotenuse:

Expand the squares to get

Bring everything to the right hand side to get

Divide both sides by 8:

This equation has solutions

This solutions would yield the following side lengths:

Since we can’t have negative side lengths, we can only accept the solution x=9.

In fact, you can check that 18,24,30 is a pythagorean triplet, i.e.