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# rectangle

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The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle?

Feb 14, 2021

### 6+0 Answers

#1
+120287
+2

Let the original length =  L   and the original width  = W

So....after both increases we have  that

2L * 3W  =  1800

(2 * 3) * L * W    =1800

6 L * W   =1800     divide both sides  by 6

L * W   =  1800  / 6   =    300 m^2  = original area

Feb 14, 2021
#2
+2184
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Let's decide that the original length of a rectangle is x, and the original width is y.

We can write an equation.

2x times 3y = 1800

6xy=1800

xy=300

300 is the original area!

Feb 14, 2021
#3
+120287
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THX, Cal ......good to see  you  !!!

CPhill  Feb 14, 2021
#4
+1

but flec got perfect score on IMO!!!

:omighty:

I am the humble Mat Hayden

If the length of the rectangle is x2, and width is x3, then a trick is to note that the original rectangle can tile the new one 2*3=6 times. So if the new rectangle has an area of 1800 m^2, the original one would have an area of 1800/6=300 m^2.

Guest Feb 14, 2021
#5
+2184
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CPhill, You too, thank you!

CalTheGreat  Feb 15, 2021
edited by CalTheGreat  Feb 15, 2021
#6
+2184
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I did NOT get a perfect score on the IMO, I didn't even enter

Nice answer Math Hayden

CalTheGreat  Feb 15, 2021