Question

One leg of a right triangle is 7 inches longer than the other leg, and the hypotenuse is 35 inches. Find the lengths of the legs of the triangle.

Answer 1

Answer: 21, 28

Explanation:

• Side #1 = x
• Side #2 = x + 7
• Hypotenuse = 35

Use the Pythagorean Theorem
`a^(2)+b^(2)=c^(2)`:

• a = x
• b = x + 7
• c = 35

Substitute in the values & solve:

`x^(2)+(x+7)^(2)=35^(2)\\x^(2)+x^(2)+14x+49=1225\\2x^(2)+14x+49-1225=0\\2x^(2)+14x-1176=0\\2(x^(2)+7x-588)=0\\2(x + 28)(x - 21)=0\\x_(1)=-28, x_(2)=21`

-28 is not a possible solution since you can't have negative inches...

• a = x = 21
• b = x + 7 = 21 + 7 = 28
• c = 35