Question

A boat’s sail is a right triangle. The length of one side of the sail is 7 feet more than the other side. The hypotenuse is 13 feet. Find the lengths of the two sides of the sail.

Answer 1

Answer: the other two sides are 5 feet and 12 feet

Explanation:

Length of one side be x , that means the other side is x + 7

by Pythagoras theorem:

`x^(2)` +
`(x+7)^(2)` =
`13^(2)`

expanding , we have:

`x^(2)` +
`x^(2)`+ 14x + 49 = 169

`2x^(2)` + 14x + 49 - 169 = 0

`2x^(2)` + 14x - 120 = 0

divide through by 2 , we have

`x^(2)`+ 7x - 60 = 0

By factorizing , we have

(x - 5)(x+12) = 0

Therefore:

x = 5 or x = -12

Since , the side can not be negative , so

x = 5

That means the other side will be 5+ 7 = 12