The width of the rectangle is 12 cm less than its length. If the perimeter of the rectangle is 120 cm, then its area is?

| June 15, 2021 | education

Let’s denote the width of the rectangle by x cm.

By the condition of the problem, the length of the rectangle is 12 cm longer than the width, that is, the length of the rectangle is (x + 12) cm.

The perimeter of the rectangle is 120 cm, that is, the doubled sum of the two sides is equal to 120.

Find the sum of the length and width of the rectangle by dividing its perimeter by 2:

120: 2 = 60 (cm).

Knowing the sum of the length and width, we compose and solve the equation:

x + x + 12 = 60.

Let’s transfer the known values ​​to one side:

2 x = 60 – 12.

2 x = 48.

x = 24.

The width of the rectangle is 24 cm.

Find the length if it is 12 cm more than the width: 24 + 12 = 36 (cm).

We calculate the area of ​​a rectangle with sides of 24 cm and 36 cm:

S = 24 * 36 = 864 (cm²).

Answer: 864 cm².



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