SOLUTION: the length of one leg of a right triangle is 10 ft. the length of the hypotenuse is 2 feet longer than the other leg. find the length of the hypotenuse and the other leg the le

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Question 263161: the length of one leg of a right triangle is 10 ft. the length of the hypotenuse is 2 feet longer than the other leg. find the length of the hypotenuse and the other leg
the length of the hypotenuse=?? ft
the lenght of the other leg=?? ft
Found 3 solutions by palanisamy, drk, mananth:
Answer by palanisamy(496) About Me  (Show Source):
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Given, the length of one leg of a right triangle is 10 ft. the length of the hypotenuse is 2 feet longer than the other leg.
Let the length of the other leg be x
The the length of the hypotenuse = x+2
In the right triangle, 10^2+x^2 = (x+2)^2
100+x^2 = x^2+4x+4
100-4 = 4x
4x = 96
x = 96/4
x = 24
So, the length of the other leg = 24 feet
The the length of the hypotenuse = x+2= 24+2 = 26 feet

Answer by drk(1908) About Me  (Show Source):
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Let a = 10, b = x and c = x+2. Using Pythagorean theorem we get
a%5E2+%2Bb%5E2+=+c%5E2
and then
10%5E2+%2B+x%5E2+=+%28x%2B2%29%5E2
expanding, we get
100+%2B+x%5E2+=+x%5E2+%2B+4x+%2B+4
subtracting x^2, we get
100+=+4x+%2B+4
solving, we get
4x+=+96
and then
x+=+24
the sides become
10, 24, 26

Answer by mananth(16946) About Me  (Show Source):
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the length of one leg of a right triangle is 10 ft. the length of the hypotenuse is 2 feet longer than the other leg. find the length of the hypotenuse and the other leg
let the other leg be x
one leg =10
length of hypotenuse x+2
x^2+10^2=(x+2)^2
x^2+100=x^2+4x+4
4x=100-4
X= 100-4/ 4
X= 24
Hypotenuse= 26