SOLUTION: The area of a rectangular cutting board is 330 square inches.The perimeter is 74 inches.What are the dimensions of the cutting board? inches by inches.
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Question 1206410: The area of a rectangular cutting board is 330 square inches.The perimeter is 74 inches.What are the dimensions of the cutting board? inches by inches.
Found 3 solutions by math_tutor2020, MathLover1, greenestamps:
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
L = length
W = width
2(L+W) = perimeter = 74
2(L+W) = 74
L+W = 74/2
L+W = 37
L = 37-W
L*W = area
(37-W)*W = 330
-W^2 + 37W - 330 = 0
W^2 - 37W + 330 = 0
Apply the quadratic formula (when a = 1, b = -37, c = 330)
or
or
or
If W = 22, then L = 37-W = 37-22 = 15
And vice versa if W = 15 then it leads to L = 22.
The order of L and W doesn't matter.
Check:
perimeter = 2*(L+W) = 2*(22+15) = 74
area = L*W = 22*15 = 330
Everything is confirmed.
Answer: 22 inches by 15 inches
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
given:
in^2
since , we have
...solve for
.....eq.1
in
since , we have
.......solve for
.......eq.2
from eq.1 and eq.2 we have
.......solve for
....factor
=> or=>preferred for width
go to
.......eq.2, substitute
answer: the dimensions of the cutting board are by
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The perimeter is 74 inches, so length plus width is 37 inches; the area is 330 square inches.
;
Solving the first equation for one of the variables and substituting in the second equation gives you a quadratic equation.
Any quadratic equation can be solved using the quadratic formula, as one of the tutors did.
The quadratic equation in this problem can also be solved by factoring, because the numbers are "nice"; the other tutor solved the problem that way.
However, solving the problem by factoring requires finding two numbers whose sum is 37 and whose product is 330 -- which is what the original problem requires.
So, if a formal algebraic solution is not required, the fastest way to solve the problem is by trial and error. Look at pairs of whole numbers whose product is 330 and find one for which the sum is 37.
33 and 10 is one easily found pair with a product of 330; but the sum is 43, which is too large. That means the two numbers we are looking for have to be closer together than 33 and 10.
A little mental arithmetic can then find 22 and 15, for which the sum is the required 37.
ANSWER: 22 inches by 15 inches
NOTE on finding the second pair of numbers with a product of 330, having found the first one....
We know the two numbers must be closer together than 33 and 10, so the 33 has to be smaller and the 10 has to be larger. Seeing that 33 is a multiple of 3, we can make it smaller by multiplying it by 2/3, which means we have to multiply the 10 by 3/2 to keep the same product. That gives us the numbers 22 and 15, which are the numbers we are looking for.
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