The area of a rectangular shop in the mall is 136 square meters. The perimeter is 50 meters. What are the dimensions of the shop?

Question

Help urgent, bad math homework and was not taught it!

Answer 1

First list your known equations,(lenth=L, width=w): area=L* w perimeter=2L+2w

Then plug in the info given to you into your known equations:136=L*w 50=2L+2w

Next isolate the equations to get the varibles on seperate sides ( 136=l*w (divide both sides by w) 136/w=l) (50=2L+2w (subtract 2w from both sides) 50-2w=2L (divide both sides by 2) 25-w=L)

Now, set both equations equal to each other (you can do this because they are both equal to L (transitive property)): 136/w=25-w (Multiply both sides by w) 136= 25w-w^2 (subtract 136 from both sides) 0=25w-w^2-136 (multiply by -1, and reanrrange just to be better able to visualize) 0=-w^2-25w+136 (Factor) 0=(w-8)(w-17) w=8 or w=17

Lastly, plug what you found into one of the equations to get the other variable.: 136=L(8) (divide both sides by 8) L=17

The dimensions of the shop is 8 meters by 17 meters (use the same units as the question)

(To check plug into the other equation 136=17*8 136=136 50=2(17)+2(8) 50=50)

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