The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches. then the area of the resulting rectangle is 24 square inches What is the area of the original rectangle?

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The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches. then the area of the resulting rectangle is 24 square inches What is the area of the original rectangle?

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Answer 1 · 2017-11-20T13:36:46

$48 square inches$ $48" square inches"$

Explanation:

$let the width = n$ $"let the width "=n$

$then length = n + 2$ $"then length "=n+2$

$n and n + 2 are consecutive even integers$ $n" and "n+2color(blue)" are consecutive even integers"$

$the width is decreased by 3 inches$ $"the width is decreased by " 3" inches"$

$\Rightarrow width = n - 3$ $rArr"width "=n-3$

$area = length \times width$ $"area "="length "xx" width"$

$\Rightarrow (n + 2) (n - 3) = 24$ $rArr(n+2)(n-3)=24$

$\Rightarrow n^{2} - n - 6 = 24$ $rArrn^2-n-6=24$

$\Rightarrow n^{2} - n - 30 = 0 \leftarrow in standard form$ $rArrn^2-n-30=0larrcolor(blue)"in standard form"$

$the factors of - 30 which sum to - 1 are + 5 and - 6$ $"the factors of - 30 which sum to - 1 are + 5 and - 6"$

$\Rightarrow (n - 6) (n + 5) = 0$ $rArr(n-6)(n+5)=0$

$equate each factor to zero and solve for n$ $"equate each factor to zero and solve for n"$

$n - 6 = 0 \Rightarrow n = 6$ $n-6=0rArrn=6$

$n + 5 = 0 \Rightarrow n = - 5$ $n+5=0rArrn=-5$

$n > 0 \Rightarrow n = 6$ $n>0rArrn=6$

$the original dimensions of the rectangle are$ $"the original dimensions of the rectangle are"$

$width = n = 6$ $"width "=n=6$

$length = n + 2 = 6 + 2 = 8$ $"length "=n+2=6+2=8$

$6 and 8 are consecutive even integers$ $6" and "8" are consecutive even integers"$

$\Rightarrow original area = 8 \times 6 = 48 square inches$ $rArr"original area "=8xx6=48" square inches"$

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The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches. then the area of the resulting rectangle is 24 square inches What is the area of the original rectangle?

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Explanation:

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