Question
In a rectangle, one side is 7 cm longer than the other and the diagonal is 13 cm. Calculate the area of the rectangle
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Answer to a math question In a rectangle, one side is 7 cm longer than the other and the diagonal is 13 cm. Calculate the area of the rectangle
Fred
4.4120 Answers
Let one side of the rectangle be x cm, then the other side will be (x+7) cm.
We know that the diagonal of a rectangle forms a right triangle with the sides of the rectangle. So, we can use the Pythagorean theorem to find the relationship between the sides of the rectangle:
x^2 + (x+7)^2 = 13^2
Expanding and simplifying:
x^2 + x^2 + 14x + 49 = 169
2x^2 + 14x - 120 = 0
Dividing the equation by 2 to simplify:
x^2 + 7x - 60 = 0
Factoring the quadratic equation:
(x+12)(x-5) = 0
So, x = 5 cm (as the side length of a rectangle can't be negative).
Therefore, the sides of the rectangle are 5 cm and 12 cm.
The area of a rectangle is given by the formula:Area = length \times width
Therefore, the area of the rectangle is:
Area = 5 \times 12 = 60 \, cm^2
\boxed{60 \, cm^2}
We know that the diagonal of a rectangle forms a right triangle with the sides of the rectangle. So, we can use the Pythagorean theorem to find the relationship between the sides of the rectangle:
Expanding and simplifying:
Dividing the equation by 2 to simplify:
Factoring the quadratic equation:
So, x = 5 cm (as the side length of a rectangle can't be negative).
Therefore, the sides of the rectangle are 5 cm and 12 cm.
The area of a rectangle is given by the formula:
Therefore, the area of the rectangle is:
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