# The perimeter of the rectangle is 28 and the diagonal is 10. Find the area of this rectangle.

June 30, 2021 | education

| Let’s denote the sides of the rectangle a and b.

S = a * b

By the Pythagorean theorem a ^ 2 + b ^ 2 = 10 ^ 2

The perimeter is found by the formula:

P = 2 (a + b)

2 (a + b) = 28.Therefore: a + b = 14

Let’s square (a + b). We get:

(a + b) ^ 2 = 14 ^ 2

(a + b) ^ 2 = 196

Expand the brackets:

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

We know a ^ 2 + b ^ 2 = 100

Then we get:

2ab + 100 = 196

2ab = 96

ab = 48

Answer: S = 48

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.