Question

Question #c477a

Answer 1

The new width `= 16` metres and new length `= 24` metres

Explanation:

There are two different rectangles to consider. Once we have have chosen a variable, we can write an expression for each side of the rectangles in term of that variable.

Let the width of the smaller garden be `x`
The length is `4m` longer, which gives `x+4`

The shorter perimeter will be `2 (x+x+4) = 4x+8`

For the larger garden, the width is `x+8`
and the length is `x+4 +12 = x+16`

The longer perimeter will be `2(x+8+x+16) = 4x +48`

The bigger perimeter is twice as big as the smaller:

[`2` times smaller = bigger]

`2(4x+8) = 4x+48" "div 2`

`4x+8 = 2x +24`

`2x = 16`

`x =8`

The old garden has width =`8` and length = `12`

The new garden has width `= 16`metres

and length `= 24` metres