Answer:
5 by 12
Step-by-step explanation:
The area and perimeter formulas can be used to write simultaneous equations for the dimensions of the rectangle. Solving those will give the dimensions of a rectangle with area 60 and perimeter 34.
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The relevant formulas for area (A) and perimeter (P) in terms of length (L) and width (W) are ...
A = LW
P = 2(L +W)
Using the given information, we can find a quadratic in W that will tell us the dimensions.
34 = 2(L +W) ⇒ L = 17 -W
60 = LW = (17-W)(W)
W² -17W +60 = 0 . . . . . written as a quadratic in standard form
This equation can be solved by factoring and using the zero product rule.
(W -12)(W -5) = 0
Values of W that make these factors zero are ...
W = 12 or W = 5
For W = 12, L = 17 -12 = 5.
For W = 5, L = 17 -5 = 12.
The dimensions of the rectangle are 5 by 12.
