# Find the area of a square if its sides are 3: 4, and the diagonals = 15 cm.

October 8, 2021 | education

| From the condition it is known that the sides of the rectangle are 3: 4, and it is also known that the diagonals of the rectangle are 15 cm.

To find the area of a rectangle, we will apply the formula:

S = a * b;

First of all, we find the sides of the rectangle. Let’s apply the Pythagorean theorem for this. Consider a right-angled triangle formed by the sides of the rectangle and the diagonal.

3k and 4k sides and 15 – hypotenuse.

(3k) ^ 2 + (4k) ^ 2 = 15 ^ 2;

9k ^ 2 + 16k ^ 2 = 225;

25k ^ 2 = 225;

k ^ 2 = 9;

k = 3.

The sides are 3 * 3 = 9 and 4 * 3 = 12.

S = 9 * 12 = 108 cm ^ 2.

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