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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