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a rectangle is 3 times as long as it is wide and its perimeter is 120 centimeters. find area.

Sagot :

brookegallagher
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
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.
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