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

Step-by-step 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