The longer leg of a right triangle is 4inches longer than the shorter leg. The hypotenuse is 8inches longer than the shorter leg.

Question

The longer leg of a right triangle is
4inches
longer than the shorter leg. The hypotenuse is
8inches
longer than the shorter leg. Find the side lengths of the triangle.

 

SHORTER LEG = 

LONGER LEG =

HYPOTENUSE =

Answer 1

Let a = short leg of the right triangle, b = the longer leg, and c = the hypotenuse.

• The longer leg of a right triangle is 4inches longer than the shorter leg: b = a + 4
• The hypotenuse is 8inches longer than the shorter leg:  c = a + 8

 

Use the Pythagorean Theorem:

 

a² + b² = c²

a² + (a+4)² = (a+8)²

a² + a² + 8a + 16 = a² + 16a + 64

a² - 8a - 48 = 0

 

Factors to:

 

(a-12)(a+4) = 0

a = 12, -4

 

Since we can't have a side of -4, a = 12

• Shorter Leg = 12 inches
• Longer Leg = 12 + 4 = 16 inches
• Hypotenuse = 12 + 8 = 20 inches

 

Answer 2

Deleted due to misreading the question, sorry if this confused you.