Question

If the diagonal of a rectangle is 3 times its smallest side, then the ratio of its sides is: Option 1: 1:2 Option 2: 1:3 Option 3: 1:4 Option 4: 1:5

Answer 1

The ratio of the sides of the rectangle is 1:2.

Step-by-step explanation:

The ratio of the sides of the rectangle is 1:2.

Let's assume that the smallest side of the rectangle is 'x'. Since the diagonal is 3 times the smallest side, it can be represented as 3x.

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (sides of the rectangle). So, we have:

x^2 + x^2 = (3x)^2

Simplifying the equation, we get:

2x^2 = 9x^2

Dividing both sides of the equation by x^2, we get:

2 = 9

This is not true, so our assumption that the ratio of the sides is 1:3 is incorrect. Therefore, the correct ratio is 1:2.

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