The diagonal of the square is 8. Find the area and perimeter of the square.
| December 12, 2020 | education
Two isosceles right-angled triangles formed in the square. By the Pythagorean theorem:
Hypotenuse squared = the sum of the squares of the legs
Let’s designate the side in the square as x, then:
8 * 8 = x2 + x2
64 = 2×2
x2 = 32
x = √32
x = 4√2
Then perimeter = 4√2 + 4√2 = 8√2
Area = 4√2 * 4√2 = 16 * 2 = 32
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