The area of a rectangle is 46 square inches. If the length is 4 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.
Answers
Let w = the width of the given rectangle.
Let l = the length of the given rectangle.
Since the length l is 3 times the width, then l = 3w.
The formula for the area A of a rectangle is: A = lw.
It's given that the area A = 60 square inches (in²); therefore,
substituting into the formula for the area of a rectangle, we have:
A = lw
60 in² = (3w)(w)
60 in² = 3w²
(60 in²)/3 = (3w²)/3
(60/3) in² = (3/3) w²
20 in² = (1) w²
w² = 20 in²
√(w²) = ±√(20) in.
√(w²) = √(20) in.
w = √(20) in.
Note: We chose the positive square root since you can't physically have a negative measurement (width)!
w = √[(4)(5)] in.
w = √4√5 in. by a property of radicals which allows √(ab) = √a√b, where a and b are non-negative real numbers.
w = 2√5 in.
Therefore, ...
l = 3w
= 3(2√5 in.)
= [(3)(2)]√5 in.
= 6√5 in.
CHECK:
A = lw
60 in² = (6√5 in.)(2√5 in.)
60 in² = (6√5)(2√5) in²
60 in² = (6)(2)(√5)(√5) in²
60 in² = (6)(2)(√25)in²
60 in² = (12)(√25)in²
60 in² = (12)(5)in²
60 in² = 60 in²
Therefore, the dimensions of the given rectangle are: the width w = 2√5 in. (exact) or 4.472 in. (rounded to 3 decimal places), and the length l = 6√5 in. (exact) or 13.416 in. (rounded to 3 decimal places)
5.1K views · Answer requested by Alicia Sanders
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