Question 452194: a rectangle has a length of 18 inches more than three times its height. the perimeter is 428, what are the dimensions?
Answer by Leaf W.(135)   (Show Source):
You can put this solution on YOUR website! "a rectangle has a length of 18 inches more than three times its height."
height: x
"three times its height": 3x
"18 inches more than three times its height": 3x + 18
therefore, length: 3x + 18
The perimeter or a rectangle is denoted as 2(length) + 2(height). If the height is x and the length is 3x + 18, then the perimeter is 2(3x + 18) + 2(x). Since the problem states that the perimeter is 428 inches:
2(3x + 18) + 2x = 428
Distribut the 2 into the 3x and 18:
6x + 36 + 2x = 428
Add like terms (6x and 2x):
8x + 36 = 428
Subtract 36 from both sides:
8x = 392
Divide both sides by 8:
x = 49
So, the height of the rectangle is 49 inches. You can plug this value for x into the expression for length (3x + 18) to find the length of the rectangle.
3x + 18
3(49) + 18
147 + 18
165
So, the length of the rectangle is 165 inches.
==> Therefore, the height of the rectangle is 49 inches and the length of the rectange is 165 inches.
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