Find the area of a rectangle if its perimeter is 80 and the aspect ratio is 2: 3

1. Vertices of the rectangle – A, B, C, D. S – area of the rectangle. AB / AD = 2/3. P = 80 units of measure – the perimeter of the rectangle.

2. AB / AD = 2/3 (according to the problem statement).

3AB = 2AD.

AB = 2AD / 3.

3. P = 2 (AB + AD) = 80 units of measurement.

AB + AD = 40 units. We substitute here 2AD / 3 instead of AB:

2АD / 3 + АD = 40 units of measurement.

5AD = 120 units.

AD = 24 units.

AB = 2 x 24/3 = 16 units.

S = AD x AB = 24 x 16 = 384 units ².




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