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

Step-by-step 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