# The length of one leg of a right triangle is 8ft.The length of hypotenuse is 4 ft longer than the other leg.What are the lengths of hypotenuse and the other leg?

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### 3 Answers

Use the Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the length of the legs and c is the hypotenuse.

Substitute 8 in for a.

8^2 + b^2 = c^2

You are given that the hypotenuse is 4 ft longer than the other leg, therefore c = b + 4. Substitute b + 4 in for c.

64 + b^2 = (b + 4)^2

Use FOIL to expand.

64 + b^2 = b^2 + 8b + 16

Subtract b^2 from both sides.

64 = 8b + 16.

Subtract 16 from both sides.

48 = 8b

Divide both sides by 8.

6 = b

c = b + 4 = 6 + 4 = 10

**length of other leg = 6 ft**

**length of hypotenuse = 10 ft**

## The length of one leg of a right triangle is 8ft.The length of hypotenuse is 4 ft longer than the other leg.

Simply use Pathagorean Thrm.

a^2 + b^2 = c^2

a&b are the legs and c is the hypotenuse

8^2 + b^2 = (b+4)^2

64 + b^2= (b+4)^2

64 + b^2= b^2+8b+ 16

subtract b^2 from both sides

64= 8b +16

subtract 16 from both sides

48 = 8b

divide both sides by 8

6=b

Take b=6 and plug it back into the original equation to figure out the hypotenuse.

8^2 + 6^2 = (6+4)^2

hypotenuse is 6+4 = 10 ft

lenth of leg b = 6 ft

The length of the other leg is x and the length of hypotenuse is (x+4)

We'll apply Pythagorean identity in the given right angle triangle:

x^2 + 8^2 = (x+4)^2

We'll expand the binomial form the right side, using the formula:

(a+b)^2 = a^2 + 2ab + b^2

x^2 + 64 = x^2 + 8x + 16

We'll eliminate x^2 both sides:

8x - 64 + 16 = 0

8x = 48

x = 6 ft

The hypotenuse is x+4 = 6+4 = 10 ft

**The requested lengths of the other leg and the hypotenuse are: 6ft and 10ft.**