1. ## rectangle area problem

a rectangle is 2 metres longer than it is wide. If each side gets increased by 2 metres, then the area increases by 16 square metres. find the dimension of the rectangle?

so $\displaystyle A = Height \cdot Width$

$\displaystyle A = (x+2)x$

$\displaystyle 16^2 = (x+4)(x+2)$

is this the appropriate calculations to be done? how should i go about it for the rest . any help?

2. Originally Posted by jvignacio
a rectangle is 2 metres longer than it is wide. If each side gets increased by 2 metres, then the area increases by 16 square metres. find the dimension of the rectangle?

so $\displaystyle A = Height \cdot Width$

$\displaystyle A = (x+2)x$

$\displaystyle 16^2 = (x+4)(x+2)$

is this the appropriate calculations to be done? how should i go about it for the rest . any help?
Your question doesn't state that the area is 16 mē but that the area increases by 16 mē.

Therefore the equation should be:

$\displaystyle A+16 = (x+4)(x+2)$ ........ Remark: The 16 isn't squared, only the dimension of this value is mē

Now plug in the term for A:

$\displaystyle (x+2)x + 16 = (x+4)(x+2)$

Expand the brackets, collect like terms, ... in short: Solve for x.

I've got x = 2

3. Originally Posted by earboth
Your question doesn't state that the area is 16 mē but that the area increases by 16 mē.

Therefore the equation should be:

$\displaystyle A+16 = (x+4)(x+2)$ ........ Remark: The 16 isn't squared, only the dimension of this value is mē

Now plug in the term for A:

$\displaystyle (x+2)x + 16 = (x+4)(x+2)$

Expand the brackets, collect like terms, ... in short: Solve for x.

I've got x = 2
cheers mate now i understand

4. Originally Posted by earboth
Your question doesn't state that the area is 16 mē but that the area increases by 16 mē.

Therefore the equation should be:

$\displaystyle A+16 = (x+4)(x+2)$ ........ Remark: The 16 isn't squared, only the dimension of this value is mē

Now plug in the term for A:

$\displaystyle (x+2)x + 16 = (x+4)(x+2)$

Expand the brackets, collect like terms, ... in short: Solve for x.

I've got x = 2
ive got x = 2 and 6 ?

5. Originally Posted by jvignacio
ive got x = 2 and 6 ?
Well, this is the abbreviated version of the sentence:

The original rectangle has a width of 2 and a length of 4 while the greater rectangle has a width of 4 and a length of 6.

I hope that you meant this