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KATRIN_1 [288]
3 years ago
10

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

Mathematics
2 answers:
Tema [17]3 years ago
7 0

Answer:

• width is y metres

• length is (2 + y) metres

{ \tt{area = length \times 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{ \frac{13}{6} }} \\  \\  = { \underline{ \underline{ \rm{ \: 3 \: strips \:  \: }}}}

PtichkaEL [24]3 years ago
3 0

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\sqrt{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 \dfrac{19.2}{13}

\\ \sf\longmapsto 1.47strips

  • She needs 2 strips
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