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A rectangle has length 2x and width x. If each diagonal of t

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A rectangle has length 2x and width x. If each diagonal of t [#permalink] New post   28 Jan 2020, 16:42
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A rectangle has length 2x and width x. If each diagonal of the rectangle has length d, what is the area of the rectangle, in terms of d?

A. \(\frac{2}{5} d\)

B. \(\frac{5}{2} d\)

C. \(\frac{4}{25} d^2\)

D. \(\frac{2}{5} d^2\)

E. \(\frac{2}{3} d^2\)

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Re: A rectangle has length 2x and width x. If each diagonal of t [#permalink] New post   29 Jan 2020, 04:30
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A rectangle has length 2x and width x. If each diagonal of the rectangle has length d, what is the area of the rectangle, in terms of d?

A. \(\frac{2}{5} d\)

B. \(\frac{5}{2} d\)

C. \(\frac{4}{25} d^2\)

D. \(\frac{2}{5} d^2\)

E. \(\frac{2}{3} d^2\)

Kudos for the right answer and explanation



Since the sides of the rectangle are 2x and x, we have:

Diagonal = \(d = \sqrt{(2x)^2 + x^2} = x\sqrt{5}\)


Area of the rectangle = \((2x)*(x) = 2x^2\)

We have:

\(d^2 = 5x^2\)
\(=> x^2 = d^2/5\)

=> Area \(= 2x^2 = 2d^2/5\)


Answer D
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Re: A rectangle has length 2x and width x. If each diagonal of t [#permalink] New post   03 Mar 2022, 08:11
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Re: A rectangle has length 2x and width x. If each diagonal of t [#permalink]
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