The length and width of a rectangle whose perimeter is 60 cm are in the ratio 3 : 2. What is the area of the rectangle?



The length and width of a rectangle whose perimeter is 60 cm are in the ratio 3 : 2. What is the area of the rectangle?

Answer:

216cm²

Step-by-step explanation:

Lets have the ratio as an equation:

3x : 2x

The perimeter of a rectangle is 2 * (length + width)

We can then substitute length and width with the given x.

2 * (3x + 2x) = 60cm

2 * 5x = 60

5x = 60/2

5x = 30

x = 6

We can then check our work by replacing x with 6

3 * 6 = 18

2 * 6 = 12

18 : 12 = 3 : 2 (check)

2 * (18 + 12) = 2 * 30 = 60 (check)

We then know area is solve using length times width.

18 * 12 = 216cm²


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