# The length of the rectangle is 4 dm. What is the area of a rectangle if its perimeter is 104 cm?

January 13, 2021 | education

| For the convenience of calculations, we will express all the parameters of the rectangle in the same units of measurement – in centimeters. One decimeter has 10 centimeters, therefore, multiply the length of the rectangle by 10:

4 dm = 4 * 10 = 40 cm.

To determine the area, we need to find out the width. The perimeter of a rectangle is the sum of the length and width times two. Let’s write this expression:

104 = 2 (40 + b), where b is the width of the rectangle.

Find b from this equation:

104 = 80 + 2b;

2b = 104 – 80;

2b = 24;

b = 12 cm width of the rectangle.

Now we can find the area. We multiply the length and width of the rectangle:

40 * 12 = 480 cm2

Answer: the area of the rectangle is 480 cm2.

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