Answer:
6 feet long and 5 feet wide.
Explanation:
Given that the formula for area is:
A=Length x Width
And perimeter is:
P= 2L + 2W
We know area is 30 and perimeter is 22, so our equations are:
30= L * W
22 = 2L + 2W
To solve as a system of equations, lets isolate L on the second equation.
22 = 2L + 2W
22 - 2W = 2L
Divide both sides by 2
11 - W = L
Inserting it into the first equation
30 = (11 - W) W
30 = 11W - W²
This looks like a quadratic, so let's bring everything to the left side and factor.
W² - 11W + 30 = 0
(W - 6) (W - 5)=0
W= 6 or W= 5
Insert both of these into 30 = L*W to find L
30 = 6L
L= 5 when W = 6
or 30 =5L
L= 6 when W = 5
Hence, the mirror is 6 feet long and 5 feet wide.
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