If a rectangle is twice as long as it is wide and has a perimeter of 30 inches, what is the area of the rectangle?

50

Explanation

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w.
The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 inches so the equation becomes: 2w + 2h = 30.
Putting these two equations together and solving for width (w):
2w + 2h = 30
w + h = 30 / 2
w + h = 15
w = 15 – h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 15 - 2w
3w = 15
w = 15 / 3
w = 5
Since h = 2w that makes h = 10 and the area \(5 \times 10 = 50\)

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