Question

The perimeter of a rectangle campsite is 64m and it’s area is 207msquare. Find the length and the breadth of the campsite

Answer 1

Answer :

$given \: perimeter \: of \: rectangle \: = \: 64m \\ \\ given \: area \: of \: rectangle \: = \: {207m}^{2} \\ \\ = > \: let \: length \: be \: l \\ \\ = > breadth \: be \: b \\ \\ = > \: as \: we \:know \: that \\ \\ = > \:l \times b \: = \: area \: of \: rectangle \\ \\ = > \: 2(l + b) = perimeter \: of \: rectangle$ = > \: $therefore \\ \\ = > \: \binom{2(l + b) = 64}{lb = 207} \\ \\ = > \: \binom{2l + 2b = 64}{lb \: = 207} \\ \\ = > \: solve \: for \: l \\ \\ = > \: 2l = 64 - 2b \\ \\ = > \: l = 32 - b \\ \\ = > \: \binom{l = 32 - b}{lb = 207}$ \\ \\ = > \: $substitute \: the \: value \: of \: l \: in \: the \: equation \: lb \: = 207 \: \\ \\ = > \: (32 - b)b = 207 \\ \\ = > \: solve \: for \: b \: \\ \\ = > \: 32b - {b}^{2} = 207 \\ \\ = > \: 32b - b {}^{2} - 207 = 0 \\ \\ = > \: - b {}^{2} + 32b - 207 = 0 \\ \\ = > \: b {}^{2} - 32b + 207 = 0 \\ \\ = > \: b = \frac{ - ( - 32) + \sqrt{( - 32) {}^{2} - 4 \times 1 \times 207} }{2 \times 1} \\ \\ = > \: b \: = \frac{32 + \sqrt{1024 - 824} }{2} \\ \\ = > \: b \: = \frac{32 + \sqrt{196} }{2} \\ \\ = > b \: = \frac{32 + 14}{2} \\ \\ = > b = 23$\\ \\ = > $substitute \: the \: value \: of \: b \: in \: the \: equation \: l = 32 - b \\ \\ = > l = 32 - 23 \\ \\ = > l = 9 \\ \\ = > \: therefore \\ \\ length \: = 9m \: \\ breadth \: = 23 \: m \:$

Hope it would help you

Answer 2

$\mathfrak{\huge{Answer:}}$

Given that:

Perimeter = 64 m

Area = 207 sq. m

Perimeter of a rectangle = 2 ( l + b )

=》 64 = 2 ( l + b )

=》 32 = l + b

=》 32 - b = l ...(1)

Area of a rectangle = l × b

=》 207 = l × b

=》 207 / l = b ...(2)

(2) in (1)

$= > 32 - \frac{207}{l} = l \\ \\ = > 32l - 207 = {l}^{2} \\ \\ = > {l}^{2} - 32l + 207 = 0 \\ \\ factorise \: it \\ \\ = > {l}^{2} - 9l - 23l + 207 = 0 \\ \\ = >l(l - 9) - 23(l - 9) = 0 \\ \\ = > (l - 23)(l - 9) = 0 \\ \\ = > l = 23 \\ \\ acc. \: to \: (1) \\ = > 32 - b = l \\ = > 32 - b = 9 \\ = > 23 = b$


Therefore, l = 9 m
b = 23 m