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Activity Discussion Math Finding the Area of a Rectangle with a Given Perimeter and Width

• # Finding the Area of a Rectangle with a Given Perimeter and Width

Posted by on June 17, 2023 at 3:29 pm

A rectangle has a length that is x times its width. If the width is 5 units and the perimeter is 120 units. What will be the area of the rectangle ?

replied 3 months, 1 week ago 2 Members · 1 Reply
• ### Majida

Member
June 18, 2023 at 11:33 am
0

Given:
Width of the rectangle = 5 units
Perimeter of the rectangle = 120 units

Let’s assume the length of the rectangle is “x” times its width.

The formula for the perimeter of a rectangle is given by:
Perimeter = 2 × (Length + Width)

Putting in the given values, we have:
120 = 2 × (x * 5 + 5)

Simplifying, we get:
120 = 2 × (5x + 5)
120 = 10x + 10
10x = 120 – 10
10x = 110
x = 110/10
x = 11

Therefore, the length of the rectangle is 11 times its width.

Now, let’s calculate the length:
Length = x * Width Length = 11 * 5 Length = 55 units

To find the area of the rectangle, we use the formula:
Area = Length × Width

Putting in the values, we get:
Area = 55 × 5 Area = 275 square units

Hence, the area of the rectangle is 275 square units.

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