SOLUTION: 1. One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle? 2. One leg of the right triangl

Question 287323: 1. One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle?
2. One leg of the right triangle is 5 units. The hypotenuse is one unit longer than the other leg. What is the length of the hypotenuse and the other leg?
Found 3 solutions by josmiceli, texttutoring, PRMath:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
(1)
you can call the legs and
By the Pythagorean theorem:

Complete the square:

The legs are 6 ft and 8 ft
check:

OK
(2)
Call the unknown leg

the other leg is

The hypotenuse is 13 and the other leg is 12
check:

OK
Answer by texttutoring(324)   (Show Source): You can put this solution on YOUR website!
1.
Let first leg = x
second leg = x+2
Use Pythag. Theorem:

Expand the (x+2)^2 term:

Factor, by finding two numbers that multiply to -48 and add up to 2.

x=-8, or x=6
The side of a triangle can't be a negative number, so the answer must be x=6.
That means the second leg is equal to x+2=6+2=8 feet.
Leg 1 = 6 feet, Leg 2 = 8 feet, Hypotenuse = 10 feet.
Question 2)
Let x = the other leg
Hypotenuse = x+1
Use Pythag. Theorem:

Expand the left side:

So the other leg is 12 units, and the hypotenuse is 13 units.
Answer by PRMath(133)   (Show Source): You can put this solution on YOUR website!
1. One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle?

One leg of the right triangle is unknown: We'll call it "x"
The other leg is 2 feet longer than the other leg: 2 + x
The hypotenuse is 10 feet long.
You know ("c" is the hypotenuse). Now let's fill in the blank.

Now let's fill in what we know.
One leg is "x"
The other leg: 2 + x
The hypot. is: 10

(FOILED the above)

(subtracted 100 from both sides of the equation)
(combined like terms)
(factored out a 2 from everything)
(divided 2 from both sides of the equation)
= 0
x = -8 or x = 6 (disregard the -8 because a side cannot equal -8)

Does this work? If one side is 6 and the other is 2 more than 6 (or 8) and the hypotenuse is 10, then we have:

} YAY it works.

2. One leg of the right triangle is 5 units. The hypotenuse is one unit longer than the other leg. What is the length of the hypotenuse and the other leg?

One leg is 5 units: 5
The hypotenuse is 1 longer than the other leg: X+ 1
The other leg is: X

Put it all together:

Does x = 12 work?

One leg is 5
The other is 12
the hypotenuse is one more than 12: this is 13

YAY this works, too.

I hope this helps you.
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