The perimeter of the rectangle is 22 and the diagonal is √65. Find the area of this straightforward.
June 15, 2021 | education
| The square of the diagonal of a rectangle is equal to the sum of the squares of two adjacent sides:
d ^ 2 = a ^ 2 + b ^ 2;
a ^ 2 + b ^ 2 = (√65) ^ 2 = 65.
The sum of two adjacent sides of a rectangle is half the perimeter:
a + b = 22/2 = 11.
Squaring both sides of the equality, we get:
(a + b) ^ 2 = 112;
a ^ 2 + b ^ 2 +2 * a * b = 121;
65 + 2 * a * b = 121;
2 * a * b = 121 – 65 = 56;
a * b = 56/2 = 28.
The area of a rectangle is equal to the product of the lengths of two adjacent sides:
S = a * b = 28.
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