the length of a rectangle is 8 cm more than its width. if its perimeter is 56 cm, find its area.
P = 2L + 2W
56 = 2(W + 8) + 2W
56 = 2W + 16 + 2W
40 = 4W
10 = W
thank u Miss. Sue
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To find the area of a rectangle, we need to know its length and width. In this case, we are given the relation between the length and width, as well as the perimeter.
Let's denote the width of the rectangle as 'w'. We are given that the length is 8 cm more than the width, so the length can be expressed as 'w + 8'.
The formula for the perimeter of a rectangle is: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, we are given that the perimeter is 56 cm, so we can write the equation as:
56 = 2(w + 8 + w)
Simplifying the equation, we get:
56 = 2(2w + 8)
Now, let's solve for w:
56 = 4w + 16
40 = 4w
w = 10
Now that we know the width is 10 cm, we can find the length:
l = w + 8
l = 10 + 8
l = 18
The width is 10 cm and the length is 18 cm.
To find the area, we use the formula: A = l * w, where A is the area, l is the length, and w is the width.
Plugging in the values, we get:
A = 10 * 18
A = 180 cm^2
Therefore, the area of the rectangle is 180 square cm.