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?
Algebra ->
Rectangles
-> 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?
Log On
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)
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
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?
~~~~~~~~~~~~~~~~~~~
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.
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?
---------
L + W = 24
Find a pair of factors of 135 that differ by 24
check for an integer solution first.
----
1*135 NG
3*45 NG
etc
==========
Don't make it a Master's Thesis.
