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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Jsy443 on January 27, 2019, 04:22:50 pm

Title: Where do I even start?
Post by: Jsy443 on January 27, 2019, 04:22:50 pm

"The length of a rectangle is 4cm more than the width. If the length were to be decreased by 5cm and the width decreased by 2cm, the perimeter would be 18cm. Calculate the dimensions of the rectangle."

I don't understand where to start with this question. I suck at problem solving questions, so a detailed explaintion for this question will be very much appreciated. Thank you.

Title: Re: Where do I even start?
Post by: mango8 on January 27, 2019, 04:53:51 pm

First thing to remember, is for questions like these, always draw a diagram!
Here is my working, let me know if anything doesn't make sense! Hope I'm right lol :)

working out!

(https://i.imgur.com/BVvgan0.jpg)

Edit: Okay so I found the dimensions of the altered rectangle. For the original rectangle as darkz said, just sub in x=6 into (x+4)=10. So yes, original dimensions are 6cm x 10cm.

Title: Re: Where do I even start?
Post by: darkz on January 27, 2019, 05:03:39 pm

Quote from: Jsy443 on January 27, 2019, 04:22:50 pm

"The length of a rectangle is 4cm more than the width. If the length were to be decreased by 5cm and the width decreased by 2cm, the perimeter would be 18cm. Calculate the dimensions of the rectangle."

I don't understand where to start with this question. I suck at problem solving questions, so a detailed explaintion for this question will be very much appreciated. Thank you.

\[
\text{Let the width of the rectangle be }x\\
\therefore \text{the width}=x\text{ and the length}=x+4\\
\text{If we decrease the length by 5 and decrease the width by 2, then}\\
\text{width}=x-2,\,\text{length}=x+4-5=x-1\\
\begin{aligned}\\
\text{Perimeter}=2(x-2)+2(x-1)&=18\\
4x-6&=18\\
x&=6\\
\end{aligned}\\
\therefore \text{ the dimensions of the original rectangle are: } 6cm\times10cm\\
\]
Edit: fixing my latex

Title: Re: Where do I even start?
Post by: Jimmmy on January 27, 2019, 05:34:42 pm

Quote from: mango8 on January 27, 2019, 04:53:51 pm

First thing to remember, is for questions like these, always draw a diagram!
Here is my working, let me know if anything doesn't make sense! Hope I'm right lol :)

working out!

(https://i.imgur.com/BVvgan0.jpg)

Spot on working out Mango, just forgot to sub x into the original rectangle to find its dimensions.  :) Darkz got it.