The rectangle has a perimeter of 28 and an area of 13.5. Find the diagonal of this rectangle.

It is known from the condition that the perimeter of the rectangle is 28, and the area is 13.5. In order to find the diagonal of a rectangle, consider a right-angled triangle formed by the sides of the rectangle (legs) and the diagonal (hypotenuse).

We use the Pythagorean theorem to write down how to find the diagonal (hypotenuse).

c ^ 2 = a ^ 2 + b ^ 2.

The square of the hypotenuse is equal to the sum of the squares of the legs.

Let’s remember the formula for finding the area of ​​a rectangle:

S = a * b = 13.5.

Let’s remember the formula for finding the perimeter of a rectangle.

P = 2 (a + b) = 28;

a + b = 28: 2;

a + b = 14.

Let’s square the last expression:

a ^ 2 + 2ab + b ^ 2 = 196;

(a ^ 2 + b ^ 2) + 2ab = 196;

c ^ 2 + 2 * 13.5 = 196;

c ^ 2 = 196 – 27;

c ^ 2 = 169;

c = 13.

Answer: the diagonal is 13.