Respuesta :
Answer:
The length of other leg of right triangle is 20.
Step-by-step 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 [tex]h-x=32[/tex].
[tex]h=32+x[/tex]
Now, we will use Pythagoras theorem to solve for other leg of right triangle as:
[tex]48^2+x^2=(x+32)^2[/tex]
Let us solve for x.
[tex]2304+x^2=x^2+64x+32^2[/tex]
[tex]2304+x^2=x^2+64x+1024[/tex]
Cancel out [tex]x^2[/tex] from both sides:
[tex]2304=64x+1024[/tex]
[tex]64x+1024=2304[/tex]
[tex]64x=2304-1024[/tex]
[tex]64x=1280[/tex]
[tex]x=\frac{1280}{64}[/tex]
[tex]x=20[/tex]
Therefore, the length of other leg of right triangle is 20.
Answer: the length of the other leg is 20
Step-by-step 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
