Area unknown

[Lise1010]

Hi

Can anyone help me work out this question, please?


The length and width of this rectangular lawn were each an exact number of metres.
By decreasing the length by 3m and the width by 1m the area of the lawn was divided by three. Find the area of the original lawn and the greatest possible area of the new lawn.

 

[Dr.Peterson]

Hi.

What help do you need?

Please show what you have done, so we can see what method you are using, whether you are doing it correctly, and where you are stuck.

 

[Steven G]

You really do need to show your work so that we can help YOU arrive at the correct answer.

I will help you start the problem.

You do not know the length and width or the original lawn.
So call the original length L and the original width W.
What is the area of the original lawn in terms of L and W?

Now what happened to the lawn? What is the new length in terms of the original length? What do you call the new width in terms of the original width? What is the area of the new lawn?

Now that we have an expression for the area of the original lawn and an expression for the area of the new lawn how do these area compare? Can you write an equation showing this comparison?

Please post back!

 

[Steven G]

This problem is a bit more involved then I initially thought. It will even have multiple answers. One thing to note is that whatever the area of the original lawn is, it must be a multiple of three.

I am anxiously awaiting to hear replies on this problem (specially from MarkFL=inside joke).

 

[Dr.Peterson]

The length and width of this rectangular lawn were each an exact number of metres.
By decreasing the length by 3m and the width by 1m the area of the lawn was divided by three. Find the greatest possible area of the original lawn and of the new lawn.

The problem has one answer, if we make the correction I've made above (without which it is a little senseless, as the two areas are so closely related).

It results in a Diophantine equation, which can be solved if necessary by what is effectively trial and error. I was hoping the OP would respond by showing the equation and asking how to solve it for an integer.