SOLUTION: The perimeter of a rectangular cutting board is 48 inches. The area is 135 square inches. What are the dimensions of the cutting board?

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Question 1075932: The perimeter of a rectangular cutting board is 48 inches. The area is 135 square inches. What are the dimensions of the cutting board?

Found 4 solutions by math_helper, ankor@dixie-net.com, ikleyn, Alan3354:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
2(x+y) = 48 (1)
xy = 135 (2)
(1) —> x = 24-y
Plug this expression for 'x' into (2):
(24-y)y = 135



and are potential solutions
y=9 —> x=15
y=15 —> x=9
—
Answer: The cutting board is 9"x15"
—
Check: 2*(9+15) = 2*(24) = 48 (ok, perimeter checks out)
9*15 = 135 (ok, area checks out)
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
The perimeter of a rectangular cutting board is 48 inches.
2L + 2w = 48
simplify, divide by 2
L + w = 24
L = -w + 24, use this form for substitution
The area is 135 square inches.
L * w = 135
replace L with (-w+24)
(-w+24) * w = 135
-w^2 + 24w - 135 = 0
Multiply by -1
w^2 - 24w + 135 = 0
You can use the quadratic formula; a=1;=-24;c=135, but this will factor to
(w-9)(w-15) = 0
two solution
w = 9, then L = 15
w = 15, then L = 9
:
:
Check this
2(15) + 2(9) = 48
15 * 9 = 135
:


What are the dimensions of the cutting board? 15 by 9
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The perimeter of a rectangular cutting board is 48 inches. The area is 135 square inches. What are the dimensions of the cutting board?
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There is a way to solve it MENTALLY. 

From the condition, L + W =  = 24 inches, and the average of L and W is a =  = 12 in.

It is clear that the values L and W are equidistant from "a": L-a = a-W.
Let x = L-a = a-W.

Then L = a + x, W = a-x,  or  L = 12+x, W = 12-x.


For the area we have LW = 135 = (12+x)*(12-x).


Thus we have an equation for x:  = 135,   or   = 144 - 135 = 9.


Then x = 3.  Hence, L = 12+3 = 15 inches  and  W = 12-3 = 9 inches.


Answer.  The length is 15 inches. The width is 9 inches.


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The perimeter of a rectangular cutting board is 48 inches. The area is 135 square inches. What are the dimensions of the cutting board?
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L + W = 24
Find a pair of factors of 135 that differ by 24
check for an integer solution first.
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1*135 NG
3*45 NG
etc
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Don't make it a Master's Thesis.
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