The perimeter of the rectangle is 1500 cm. Its length is 150 cm greater than its width. We calculated the lengths of the sides of the 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 150 cm more than the width. If we say that one value is “by” several units more or less than another, then we are talking about addition or subtraction. Let us express the length of the rectangle, a, through the width, b:
a = b + 150.
Substituting the perimeter and the expression for side a into the formula, we solve the equation:
1500 = ((b + 150) + b) × 2,
1500 = (b + 150 + b) × 2,
1500 = (2b + 150) × 2,
1500 = 4b + 300,
4b = 1500-300,
4b = 1200,
b = 300.
Side b = 300 cm.Let’s find side a:
a = 300 + 150 = 450 cm.
Answer: the length of the rectangle is 450 cm and the width is 300 cm.
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