SOLUTION: What is the area of an isosceles right triangle with perimeter 8+4√2?

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Question 1151970: What is the area of an isosceles right triangle with perimeter 8+4√2?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
What is the area of an isosceles right triangle with perimeter 8%2B4sqrt%282%29?
Isosceles Right Triangle:
A right triangle with the two legs (and their corresponding angles) equal.
the perimeter of an isosceles triangle, the expression P=2s+%2B+b is used, where s represents the length of the two congruent sides and b represents the length of the base


use the Pythagorean Theorem, which states that s%5E2+%2B+s%5E2+=+b%5E2, to express b in terms of s
2s%5E2+=+b%5E2
sqrt%282s%5E2%29+=+b
b=s%2Asqrt%282%29
then substitute in
P=2s+%2B+b
8%2B4sqrt%282%29=2s+%2B+s%2Asqrt%282%29
8%2B4sqrt%282%29=s%282%2B+sqrt%282%29%29
s=%288%2B4sqrt%282%29%29%2F%282%2B+sqrt%282%29%29
s=4%282%2Bsqrt%282%29%29%2F%282%2B+sqrt%282%29%29
s=4cross%28%282%2Bsqrt%282%29%29%29%2Fcross%28%282%2B+sqrt%282%29%29%29
s=4
then the area of an isosceles right triangle is:
A=%281%2F2%29s%2As
A=s%5E2%2F2
A=4%5E2%2F2
A=16%2F2
A=8

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
What is the area of an isosceles right triangle with perimeter 8 + 4√2?
Let each congruent side be s

Then with this being an isosceles right triangle, hypotenuse = s+%2A+sqrt%282%29

We then get: matrix%281%2C3%2C+s+%2B+s+%2B+s+%2A+sqrt%282%29%2C+%22=%22%2C+8+%2B+4sqrt%282%29%29

matrix%281%2C3%2C+2s+%2B+s+%2A+sqrt%282%29%2C+%22=%22%2C+8+%2B+4sqrt%282%29%29

Equating the 1st terms (2s = 8), or the 2nd terms (matrix%281%2C3%2C+s+%2A+sqrt%282%29%2C+%22=%22%2C+4sqrt%282%29%29, s, or one of the equal sides = matrix%281%2C2%2C+4%2C+units%29

With each congruent side being 4,