The area of a rectangle is represented by (x^2-14x-32) square units . If the width of the rectangle is represented by (x+2) units , which ex

Question

The area of a rectangle is represented by (x^2-14x-32) square units . If the width of the rectangle is represented by (x+2) units , which expression represents the length of the rectangle

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Margaret 15 mins 2021-09-12T09:55:48+00:00 1 Answer 0

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    2021-09-12T09:57:10+00:00

    The expression for length of rectangle is (x – 16) units

    Solution:

    Given that area of a rectangle is represented by x^2-14x-32 square units

    width of the rectangle is represented by (x+2) units

    To find: length of the rectangle

    The area of rectangle is given as:

    \text { area of rectangle }=\text { length } \times \text { width }

    Substituting the values in formula, we get

    x^{2}-14x-32=\text{length} \times(x+2)  —- eqn 1

    Let us first factorise the L.H.S of eqn 1

    x^{2}-14x-32

    Break the expression into groups

    =\left(x^2+2x\right)+\left(-16x-32\right)

    \mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+2x\mathrm{:\quad }x\left(x+2\right)

    \mathrm{Factor\:out\:}-16\mathrm{\:from\:}-16x-32\mathrm{:\quad }-16\left(x+2\right)

    =x\left(x+2\right)-16\left(x+2\right)

    \mathrm{Factor\:out\:common\:term\:}x+2

    =\left(x+2\right)\left(x-16\right)

    Now substitute the above value in eqn 1

    (x + 2)(x - 16) = length \times (x + 2)

    length = \frac{(x + 2)(x - 16)}{x + 2}

    Length = x – 16

    Thus the expression for length of rectangle is (x – 16) units

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