Question

A rectangular lawn is 2 m longer than it is wide.

The area of the lawn is 21 m². The gardener wants to edge the lawn with edging strips
which are sold in lengths of 13 m. How many will she need to buy?

Answer 1

• width is y metres

• length is (2 + y) metres

`{ \tt{area = length * width}} \\ \\ { \rm{21 = (2 + y)(y)}} \\ \\ { \rm{21 = 2y + {y}^(2) }} \\ \\ { \rm{ {y}^(2) + 2y - 21 = 0 }} \\ \\ { \rm{ \dashrightarrow \: by \: factorisation : }} \\ \\ { \boxed{ \rm{y \approx4 \: and \: - 6}}}`

• Therefore, length = 4 + 2 = 6 meters

• The gardener will need;

`= { \rm{ (13)/(6) }} \\ \\ = { \underline{ \underline{ \rm{ \: 3 \: strips \: \: }}}}`

Answer 2

Let's breadth be x

• Length be x+2

ATQ

`\\ \sf\longmapsto x(x+2)=21`

`\\ \sf\longmapsto x^2+2x=21`

• Use completing the square method

`\\ \sf\longmapsto 4(x^2+2x)=4(21)`

`\\ \sf\longmapsto 4x^2+8x=84`

`\\ \sf\longmapsto (2x)^2+2(2x)(2)=84`

`\\ \sf\longmapsto (2x)^2+2(2x)(2)+2^2=2^2+84`

`\\ \sf\longmapsto (2x+2)^2=88`

`\\ \sf\longmapsto 2x+2=\pm√(88)`

• As it's dimensions we will take positive

`\\ \sf\longmapsto 2x+2\approx 9.7`

`\\ \sf\longmapsto 2x=9.7-2=7.7`

`\\ \sf\longmapsto x=3.8`

• x+2=3.8+2=5.8

Now

`\\ \sf\longmapsto Perimeter=2(L+B)`

`\\ \sf\longmapsto perimeter=2(3.8+5.8)`

`\\ \sf\longmapsto perimeter=2(9.6)`

`\\ \sf\longmapsto Perimeter=19.2m`

• Length of 1 strip=13m

Total strips

`\\ \sf\longmapsto (19.2)/(13)`

`\\ \sf\longmapsto 1.47strips`

• She needs 2 strips