The diagonal of the rectangle is 17 cm and its perimeter is 46 cm. find the sides of the rectangle

Given: AВСD – rectangle, P = 46 cm, AC = 17 cm (diagonal)

Find: AB =? BC =?

Solution: Let’s compose a system of equations, where a and b are the sides of the rectangle.

Since the perimeter is the sum of all the sides of the rectangle, we get the first equation:

2a + 2b = 46

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs, we get the second equation:

a2 + b2 = 172

From the first equation we get: a = 23 – b, substituting instead of a this expression in the second equation, we get:

(23 – b) 2 + b2 = 172;

We open the brackets, give similar terms, we get the following form of the equation:

– 2b2 + 46b – 240 = 0

We solve the quadratic equation through the discriminant, to find the discriminant we use the formula D = b2 – 4ac, substitute the values ​​of the coefficients and get the value of the discriminant:

D = 462 – 4 * (- 2) * (- 240) = 196

We find the roots of the equation using the standard formula:

x1 = – 32 / – 4 = 8; x2 = 60/4 = 15.

Answer: The sides of the rectangle are equal: 8 cm and 15 cm