The perimeter of the rectangle is 28 and the diagonal is 10. Find the area of this rectangle.
June 30, 2021 | education
| Let’s denote the sides of the rectangle a and b.
S = a * b
By the Pythagorean theorem a ^ 2 + b ^ 2 = 10 ^ 2
The perimeter is found by the formula:
P = 2 (a + b)
2 (a + b) = 28.Therefore: a + b = 14
Let’s square (a + b). We get:
(a + b) ^ 2 = 14 ^ 2
(a + b) ^ 2 = 196
Expand the brackets:
a ^ 2 + 2ab + b ^ 2 = 196
We know a ^ 2 + b ^ 2 = 100
Then we get:
2ab + 100 = 196
2ab = 96
ab = 48
Answer: S = 48
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