SOLUTION: The diagram shows an isosceles right triangle. The two legs are "x," and the hypotenuse is x radical 2. A. If its perimeter is 10, find x. B. If its area is 12, find x.

Algebra ->  Radicals -> SOLUTION: The diagram shows an isosceles right triangle. The two legs are "x," and the hypotenuse is x radical 2. A. If its perimeter is 10, find x. B. If its area is 12, find x.      Log On


   

Question 363260: The diagram shows an isosceles right triangle.
The two legs are "x," and the hypotenuse is x radical 2.
A. If its perimeter is 10, find x.
B. If its area is 12, find x.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The diagram shows an isosceles right triangle.
The two legs are "x," and the hypotenuse is x radical 2.
:
A. If its perimeter is 10, find x.
x + x + x%2Asqrt%282%29 = 10
2x + x%2Asqrt%282%29 = 10
x%2Asqrt%282%29 = -2x + 10
Square both sides
x^2(2) = (-2x+10)^2
FOIL (-2x+10)*(-2x+10)
2x^2 = 4x^2 - 20x - 20x + 100
2x^2 = 4x^2 - 40x + 100
:
Combine on the right
0 = 4x^2 - 2x^2 - 40x + 100
:
A quadratic equation
2x^2 - 40x + 100 = 0
:
Simplify, divide by 2
x^2 - 20x + 50 = 0
Use the quadratic formula to find x, a=1; b=-20; c=50
Two solutions
x = 17.06
and
x = 2.93 is the only reasonable solution
Check
2(2.93) + 2.93%2Asqrt%282%29 = 10.00
:
:
B. If its area is 12, find x.
.5(x*x) = 12
multiply both sides by 2
x^2 = 24
x = sqrt%2824%29
x = 4.9
:
Check
.5 * 4.9 * 4.9 = 12.0