Question
A rectangle's length is 4 times its width. If the area is 180 square units, find the rectangle's dimensions.
A rectangle's length is 4 times its width. If the area is 180 square units, find the rectangle's dimensions.
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Koala Tutor
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Let the width of the rectangle be x.
Then, the length of the rectangle is 4x.
The area of the rectangle is given by: length × width
So, we can write the equation:
x (4x) = 180
4x² = 180
Dividing both sides by 4, we get:
x² = 45
Taking the square root of both sides, we get:
x = ±√45
Since width cannot be negative, we take the positive square root:
x = √45
Simplifying the square root, we get:
x = 3√5
Therefore, the width of the rectangle is 3√5 units.
And the length of the rectangle is 4 times the width:
Length = 4x = 4 (3√5) = 12√5 units.
So, the rectangle's dimensions are 3√5 units by 12√5 units.
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