Question

One leg of a right triangle has a length of 48. The difference in length between the hypotenuse and the other leg is 32. Find the length of the other leg

Answer 1

Answer: the length of the other leg is 20

Explanation:

Let x represent the length of the other leg.

One leg of a right triangle has a length of 48. The difference in length between the hypotenuse and the other leg is 32. Since the Hypotenuse is the longest side of the right angle triangle, it means that

Hypotenuse = x + 32

To determine the length of the other leg, we would apply Pythagoras theorem which is expressed as

hypotenuse² = opposite side² + adjacent side²

Therefore

(x + 32)² = x² + 48²

x² + 32x + 32x + 1024 = x² + 2304

x² - x² + 64x = 2304 - 1024

64x = 1280

x = 1280/64

x = 20

Answer 2

The length of other leg of right triangle is 20.

Explanation:

Let x and h represent the length of the other leg and hypotenuse of triangle respectively.

We have been given that one leg of a right triangle has a length of 48. The difference in length between the hypotenuse and the other leg is 32. This means that length of other leg would be
`h-x=32`.

`h=32+x`

Now, we will use Pythagoras theorem to solve for other leg of right triangle as:

`48^2+x^2=(x+32)^2`

Let us solve for x.

`2304+x^2=x^2+64x+32^2`

`2304+x^2=x^2+64x+1024`

Cancel out
`x^2` from both sides:

`2304=64x+1024`

`64x+1024=2304`

`64x=2304-1024`

`64x=1280`

`x=(1280)/(64)`

`x=20`

Therefore, the length of other leg of right triangle is 20.