The perimeter is the sum of the sides
since opposite sides are = in rectangle add 2w+2l
let x=width
3x= length
8x= 120
x=15
substitute 15 for x
w=15
l= 45
area= l x w
15 x 45 = 675
area = 675 cm.
The formula for perimeter is P = 2l + 2w In this particular case you are given that the length is three times the width: 3l = w In this case, you are also given: P = 120 Therefore, 120 = 2l + 2w At this point you have a system of equations: 120 = 2l + 2w l = 3w Now you can use substitution (plug in 3w for l in the perimeter equation) 120 = 2(3w) + 2w Simplify: 120 = 6w + 2w 120 = 8w 120/8 = 8w/8 15 = w Plug in the width into one of your original equations to get the length: l = 3*15 l = 45 Now you know that l = 45 and w = 15 Now, you plug this information in for your equation for area: A = l*w A = 45*15 A = 675 The area of the rectangle is 675 cm²
