The area of the rectangle is 108 cm², and its perimeter is 42 cm. What is the diagonal of this rectangle?
| September 15, 2021 | education
The area of a rectangle is the product of its sides.
S = a * b.
The perimeter of a rectangle is twice the sum of its sides.
P = 2 * (a + b).
Substitute the area and perimeter values into the formula data.
108 = a * b.
42 = 2 * (a + b).
Find the sum of the sides of the figure.
a + b = 42/2 = 21 cm.
Let us express the value of a and substitute it into the area formula.
a = 21 – b.
108 = (21 – b) * b.
108 = 21 * b – b ^ 2.
We get a quadratic equation:
b ^ 2 – 21 * b – 108 = 0.
D ^ 2 = (21) ^ 2 – 4 * 1 * (-108) = 441 + 432 = 873.
D = 30.
b = 21 – 30/2 = 9 cm.
a = 21 – 9 = 12 cm.
Find the diagonal.
c ^ 2 = 12 ^ 2 + 9 ^ 2 = 144 + 81 = 225.
c = 15 cm.
Answer:
The diagonal is 15 cm.
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