Answer:
P = 29 units
Step-by-step explanation:
Let h represent the height of the triangle. Then 2h is the length of the base. The area is given by ...
A = 1/2bh
36 = 1/2(2h)(h) = h²
h = √36 = 6
base = 2h = 12
The base of the isosceles triangle is 12 units, and its height is 6 units.
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The altitude line makes a right angle with the base, dividing it into two right triangles with sides of length 6. The hypotenuse (s) of each of those is given by the Pythagorean theorem as ...
s = √(6² +6²) = 6√2
Then the perimeter of the triangle is ...
P = base +2s = 12 +2(6√2) = 12(1 +√2) ≈ 28.97 ≈ 29
The perimeter of the triangle is about 29 units.
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Additional comment
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides.
For an isosceles right triangle, this means the hypotenuse is √2 times the side length. (This is a useful relationship to remember, as it is used a lot in algebra and geometry problems.) The acute angles in such a triangle are 45°.
