Question

Two roads of width 5 m run perpendicular to each other in the middle of a
rectangular garden. The garden is of length 80m and width 60m. Find the
area of the road and hence the area of the remaining portion of the garden.​

Answer 1

Given Question :-

• Two roads of width 5 m run perpendicular to each other in the middle of a rectangular garden. The garden is of length 80m and width 60m. Find the area of the road and hence the area of the remaining portion of the garden.

ANSWER

$\bull \: \rm \: Length \: of \: rectangular \: field,  \: l= \: 80 \: m$

$\bull \: \rm \:Width \: of \: rectangular \: field,  \: b \: = \: 60 \: m$

$\bull \: \rm \:Length \: of \: the \: shorter \: path, \:  l_1 \: = \: 60 \: m$

$\bull \: \rm \:Width \: of \: the \: shorter \: path,  \: b_1 \: = \: 5 \: m$

$\bull \: \rm \:Length \: of \: the \: longer \: path,  \: l_12 \: = \: 80 \: m$

$\bull \: \rm \:Width \: of \: the \: longer \: path,  \: b_2 \: = \: 5 \: m$

$\bull \: \rm \:Area \: of \: shorter \: path, \:  A_1 \: = \: l_1 \: × \: b_1$

$\rm :\implies\:A_1 \: = \: 60 \: \times \: 5$

$\rm :\implies\: \boxed{ \red{ \bf \: A_1 \: = \: 300 \: {m}^{2} }}$

$\bull \: \rm \:Area \: of \: longer \: path,  \: A_2 \: = \: l_2 \: × \: b_2$

$\rm :\implies\:A_2 \: = \: 80 \: \times \: 5$

$\rm :\implies\: \boxed{ \pink{ \bf \: A_2 \: = \: 400 \: {m}^{2} }}$

$\bull \: \rm \:Area \: of \: common \: path,  \: A_3 \: = \: 5 \: × \: 5$

$\rm :\implies\: \boxed{ \blue{ \bf \: A_3 \: = \: 25 \: {m}^{2} }}$

Thus,

$\bull \: \rm \:Area \: of \: common \: path \: = A_1 \: + \: A_2 \: - \: A_3$

$\rm :\implies\:Area_{(road)} \: = 400 + 300 - 25$

$\rm :\implies\: \boxed{ \pink{ \bf \:Area_{(road)} \: = \: 675\: {m}^{2} }}$

Thus,

$\longmapsto \: \rm \: Area_{(rectangular \: garden)} \: = 80 \times 60$

$\rm :\implies\: \boxed{ \pink{ \bf \: Area_{(rectangular \: garden)} \: \: = \: 4800 \: {m}^{2} }}$

Now,

Remaining area of garden is

$\rm \: = \: Area_{(rectangular \: garden)} \: \: - \: Area_{(road)}$

$\rm \: = \: 4800 \: - \: 675$

$\rm \: = 4125 \: {m}^{2}$