Question 148002: The longer leg of a right triangle is 1cm longer than the shorter leg and the hypontenuse is 5cm, then what are the lengths of the leg?
Found 2 solutions by Alan3354, Electrified_Levi:
Answer by Alan3354(69443)   (Show Source):
Answer by Electrified_Levi(103)  (Show Source):
You can put this solution on YOUR website! Hi, Hope I can help
.
The longer leg of a right triangle is 1 cm. longer than the shorter leg and the hypontenuse is 5cm, then what are the lengths of the leg?
.
The shorter leg is represented by "x", the longer leg is (x+1)
.
We will use the Pythagorean theorem to solve for the two sides, the Pythagorean theorem equation is
.
.
"a" and "b" are the sides, "c" is the hypontenuse. We will now replace "a", "b" , and "c"
.
.
.
We will solve it even more
.
.
.
.
We will move the "25" to the left side
.
.
.
We can reduce the equation, we will divide everything by "2"
.
.
.
We can use the quadratic equation
.
.
This is the original equation using "a", "b", and "c"
.
.
.
a = 1, b = 1, c = -12
.
Now we can replace them in the quadratic equation,
.
.
.
.
.
.
.
We will use addition(if we used subtraction, the answer would be negative)
.
.
.
.
x = 3 cm.( lengths or measurements can't be negative, the other answer would be (-4) )( you can check by replacing "x" in with "3"
or "-4"
.
The shorter side was x, or 3 cm., the longer side was (x+1), or 4 cm.
.
You can check by replacing "a" and "b" in the Pythagorean theorem equation
.
.
.
.
.
Shorter side = 3 cm.
Longer side = 4 cm.
.
Hope I helped, Levi
|
|
|
