Question

Сторона прямоугольника относится к его диагонали как 4:5, а другая сторона равна 30. найдите площадь прямоугольника

Answer 1

Problem Analysis

We are given that one side of a rectangle is related to its diagonal in a ratio of 4:5, and the other side is equal to 30. We need to find the area of the rectangle.

Solution

Let's assume the length of the shorter side of the rectangle is 4x, and the length of the longer side (which is equal to the diagonal) is 5x. We are also given that the longer side (diagonal) is equal to 30.

Using the Pythagorean theorem, we can find the value of x:

x^2 + (4x)^2 = 30^2

Simplifying the equation:

x^2 + 16x^2 = 900

17x^2 = 900

x^2 = 900/17

x ≈ 6.12

Now, we can find the length of the shorter side:

4x ≈ 4 * 6.12 ≈ 24.48

And the length of the longer side (diagonal):

5x ≈ 5 * 6.12 ≈ 30.6

The area of a rectangle is given by the formula: Area = length * width.

So, the area of the rectangle is:

Area = 24.48 * 30.6 ≈ 749.09 square units

Therefore, the approximate area of the rectangle is 749.09 square units.

Conclusion

The approximate area of the rectangle is 749.09 square units.

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