The length of the rectangle is 5 times its width. the perimeter of the rectangle is 24 cm. Determine the lengths of the sides of this rectangle.
Let’s write down the formula for the perimeter of the rectangle. The perimeter of a rectangle is the sum of the length and width of the rectangle multiplied by 2:
P = (a + b) × 2,
where a is the length of the rectangle, b is the width.
The problem statement says that the length of the rectangle is 5 times the width. Let us express the length, a, through the width, b:
a = 5 × b.
Substituting the perimeter and the expression for side a into the formula, we solve the equation with one unknown:
24 = (5b + b) × 2.
24 = 6b × 2
24 = 12b
b = 24: 12
b = 2
Side b = 2 cm.Let’s find side a:
a = 5 × 2 = 10 cm.
Answer: the length of the rectangle is 10 cm, the width is 2 cm.
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