What is the dimension of the rectangle?

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What is the dimension of the rectangle?

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Answer 1 · 2018-01-19T04:30:31

Length = $10 c m$ $10cm$
Width = $6 c m$ $6cm$

Explanation:

Let the width of the rectangle be $x$ $x$ cm. Therefore, the length of the rectangle is $x + 4$ $x+4$ cm.

We know that, if we decrease the width by $2 c m$ $2cm$ and the length by $5 c m$ $5cm$ , the perimeter will be $18 c m$ $18cm$ .

That means,

$2 [(x - 2) + (x + 4 - 5)] = 18$ $2[(x-2)+(x+4-5)]=18$

$2 [(x - 2 + x - 1)] = 18$ $2[(x-2+x-1)]=18$

$2 (2 x - 3) = 18$ $2(2x-3)=18$

$2 x - 3 = 9$ $2x-3=9$

$2 x = 12$ $2x=12$

$x = 6$ $x=6$

So, the width is $6 c m$ $6cm$ long. Then, the length will be $6 + 4 = 10 c m$ $6+4=10cm$ long.

Answer 2 · 2018-01-19T09:46:48

$dimensions are 10 cm by 6 c m$ $"dimensions are "10" cm by "6" cm$

Explanation:

$let the width = w$ $"let the width "=w$

$then length = w + 4 \leftarrow 4 more than width$ $"then length "=w+4larrcolor(blue)"4 more than width"$

$decrease length by 5 \to w + 4 - 5 \to w - 1$ $"decrease length by 5 "tow+4-5tow-1$

$decrease width by 2 \to w - 2$ $"decrease width by 2 "tow-2$

$∙ perimeter = (2 \times length) + (2 \times width)$ $• " perimeter "=(2xx"length")+(2xx"width")$

$\times \times \times \times \times = 2 (w - 1) + 2 (w - 2)$ $color(white)(xxxxxxxxxx)=2(w-1)+2(w-2)$

$\times \times \times \times \times = 2 w - 2 + 2 w - 4$ $color(white)(xxxxxxxxxx)=2w-2+2w-4$

$\times \times \times \times \times = 4 w - 6$ $color(white)(xxxxxxxxxx)=4w-6$

$now perimeter = 18$ $"now perimeter "=18$

$\Rightarrow 4 w - 6 = 18$ $rArr4w-6=18$

$add 6 to both sides$ $"add 6 to both sides"$

$4wcancel(-6)cancel(+6)=18+6$

$rArr4w=24$

$"divide both sides by 4"$

$(cancel(4) w)/cancel(4)=24/4$

$rArrw=6$

$rArr"width "=6" cm "$

$rArr"length "=w+4=6+4=10" cm"$

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What is the dimension of the rectangle?

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