Thread: A rectangular lawn

A rectangular lawn 10m by 8m is surrounded by a path which is x m wide. The total area of the path and lawn is 143m^2. I have worked out the width to be 3m. Very obvious but I need a expression of how i worked this out please help!

Originally Posted by thebof1993

A rectangular lawn 10m by 8m is surrounded by a path which is x m wide. The total area of the path and lawn is 143m^2. I have worked out the width to be 3m. Very obvious but I need a expression of how i worked this out please help!

The length and width is increased by 2x if you include the path.

$\displaystyle (2x+8)(2x+10)=143$

I don't get 3 as an answer here.

no i need a expression of how to work out 3. 3 is the answer because 10 + 3 is 13 and 8 + 3 = 11. 13 x 11 = 143.

ive now worked it out!!!

(xm+10)(xm+8)=143m^2
xm^2+18xm+80=142m^2
xm^2+18xm-63= 0

you now use the quadratic formula and you get either -21 or 3 as its a physical lenght it can only be 3. and theres your answer!

Originally Posted by thebof1993

ive now worked it out!!!

(xm+10)(xm+8)=143m^2 $\displaystyle (2x+10)(2x+8)=143$
xm^2+18xm+80=142m^2
xm^2+18xm-63= 0

you now use the quadratic formula and you get either -21 or 3 as its a physical lenght it can only be 3. and theres your answer!

That's not quite correct. Remember the length and width was increased by 2x. This means the path is only 1.5 meters wide, not 3 meters. Your initial equation is incorrect.

If you solve my quadratic equation, you'll discover that x = 1.5 meters.

But if you are correct with x being equal to 1.5 then that would make:

10 + x = 11.5
8 + x = 9.5
9.5 x 11.5 = 109.25 Where as the question states that the total area is 143m. Where did u get it being raised to the two from anyway?

Originally Posted by thebof1993

But if you are correct with x being equal to 1.5 then that would make:

10 + x = 11.5
8 + x = 9.5
9.5 x 11.5 = 109.25 Where as the question states that the total area is 143m. Where did u get it being raised to the two from anyway?

It's 10+2x, not 10+x.
It's 8+2x, not 8+x.

See diagram: