The two sides of the rectangle are 35 cm each. The perimeter of the rectangle is 236 cm.

The two sides of the rectangle are 35 cm each. The perimeter of the rectangle is 236 cm. How much is the area of the rectangle?

The perimeter of any geometric shape is the sum of the lengths of its sides.

The perimeter of a rectangle is the sum of the lengths of the sides of the rectangle multiplied by 2.

P = (a + b) × 2,

where P is the perimeter of the rectangle and a and b are the sides of the rectangle.

It is known that two sides of a rectangle are 35 cm long. Suppose we are given sides b.

Let us express side a from the formula for the perimeter:

P = 2a + 2b,

2a = P – 2b,

a = (P – 2b) ÷ 2.

Let’s calculate the side a of the rectangle:

a = (236 – (2 × 35)) ÷ 2 = (236 – 70) ÷ 2 = 166 ÷ 2 = 83 cm.

We know the two sides of the rectangle.

Calculate the area of ​​the rectangle
The area of ​​a rectangle is equal to the product of the lengths of its sides. The area is designated by the letter S.

S = a × b,

where a is the length, b is the width of the rectangle.

S = 35 × 83 = 2905 cm².

Answer: the area of ​​the rectangle is 2905 cm².