The area of the rectangle is 24cm ^ 2, and its sides are in a ratio of 2: 3. What is the diagonal of the rectangle?

A rectangle is a quadrilateral in which all corners are straight, and opposite sides are parallel and equal to each other.

The area of ​​a rectangle is the product of its length and width:

S = AB * BC.

Since the sides of the rectangle are 2: 3, and the area is 24 cm2, we express:

AB – 2x;

BC – 3x;

2x * ∙ 3x = 24;

6x = 24;

x = 24/6 = 4;

AB = 2 * 4 = 8 cm;

BC = 3 ∙ * 4 = 12 cm.

In order to calculate the length of the AC diagonal, consider the triangle ΔABC. This triangle is rectangular. Let’s apply the Pythagorean theorem:

AC ^ 2 = AB ^ 2 + BC ^ 2;

AC ^ 2 = 8 ^ 2 + 12 ^ 2 = 64 + 144 = 208;

AC = √208 ≈ 14.42 cm.

Answer: The AC diagonal is 14.42 cm.