Find the area of a rectangle if its perimeter is 74cm and the difference in sides is 17cm.

univerkov | September 2, 2021 | education

1. Vertices of the rectangle – A, B, C, D. S – the area of the parallelogram. Perimeter (P) = 74 cm.

AD – AB = 17 cm.

2. AD = AB + 17 cm.

3.Considering that the sides of the rectangle opposite each other are equal, the perimeter of this geometric figure is calculated by the formula:

P = 2 (AD + AB) = 74 cm.

AD + AB = 37 cm. Substitute here AD = (AB + 17):

AB + 17 + AB = 37 cm.

2AB = 20 cm.

AB = 10 cm.

AD = 10 + 17 = 27 cm.

4. S = AD x AB = 27 x 10 = 270 cm².

Answer: S is equal to 270 cm².

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