Finding the area of a rectangle?

Question

The perimeter of a rectangle is 210cm. The ratio of the length to width is 3:4: What is the area of the sign in square centimeters?

Answer 1

Hi Jack,

The perimeter of a rectangle is twice the sum of the length and the width or 2(L+W)

We are given the perimeter so 2(L+W) = 210

Dividing both sides by 2, L+W = 105

Now the ratio of the length to the width is 3:4. This means that if the length is 3x, the width is 4x. Substituting this in the equation above

3x+4x=105

Combine like terms, 7x=105

Divide both sides by 7, x = 15

L = 3x = 3(15) = 45

W = 4x = 4(15) = 60

Now the area of a rectangle is length times width, A=LW

Area = (45)(60) = 2700 square centimeters

Answer 2

210/14=15; side "a"=45; "b"=60.

45*60=2700sq/cm