Question

If the length of a building is 2 1 2 times the width and each dimension is increased by 7 ft, then the perimeter is 266 ft. Find the dimensions of the original building in ft.

Answers

  1. Answer:

    The original dimensions of the building is 95 ft × 38 ft.

    Explanation:

    Let the original length be ‘l’ and original width be ‘w’.

    Given:

    Original length (l) = 2\frac{1}{2}\times original\ width

    Original width = ‘w’.

    So, l=2\frac{1}{2}w=\frac{5}{2}w

    Now, as per question:

    Length and width is increased by 7 ft.

    So, new length (l’) = l+7=\frac{5w}{2}+7

    New width (w’) = w+7

    New perimeter (P) = 266 ft

    Perimeter is given as:

    P=2(l' +w')\\\\266=2(\frac{5w}{2}+w)\\\\\frac{266}{2}=\frac{5w+2w}{2}\\\\266=7w\\\\w=\frac{266}{7}=38\ ft

    Therefore, original width = 38 ft.

    Original length is, l=\frac{5\times 38}{2}=\frac{190}{2}=95\ ft

    Hence, the original dimensions of the building is 95 ft × 38 ft.

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