What is the dimension of the rectangle?

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2 Answers
Jan 19, 2018

Length = #10cm#
Width = #6cm#

Explanation:

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

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

That means,

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

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

#2(2x-3)=18#

#2x-3=9#

#2x=12#

#x=6#

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

Jan 19, 2018

#"dimensions are "10" cm by "6" cm#

Explanation:

#"let the width "=w#

#"then length "=w+4larrcolor(blue)"4 more than width"#

#"decrease length by 5 "tow+4-5tow-1#

#"decrease width by 2 "tow-2#

#• " perimeter "=(2xx"length")+(2xx"width")#

#color(white)(xxxxxxxxxx)=2(w-1)+2(w-2)#

#color(white)(xxxxxxxxxx)=2w-2+2w-4#

#color(white)(xxxxxxxxxx)=4w-6#

#"now perimeter "=18#

#rArr4w-6=18#

#"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"#