Question

9. Two cross roads, each of width 5m, run at right angles through the centre of a rectangular
park of length 700 m and breadth 300 m parallel to its sides. Find the area of the roads. Also,
find the cost of constructing the roads at the rate of 105 per m​

Answer 1

Given Question :-

• Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 700 m and breadth 300 m parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of 105 per m^2.

$\large\underline\purple{\bold{Solution :- }}$

$\tt \:  Length \: of \: rectangular \: field, l= \: 700 \: m$

$\tt \:Width \: of \: rectangular \: field, b= \: 300 \: m$

$\tt \red{Length \: of \: the \: shorter \: path, l_1= \: 300 \: m}$

$\tt \: \red{</p><p>Width \: of \: the \: shorter \: path, b_1=5 \: m}$

$\tt \: \purple{Length \: of \: the \: longer \: path, l_2=700 \: m}$

$\tt \purple{ Width \: of \: the \: longer \: path,  \: b_2=5 \: m \: }$

$\tt \green{Area \: of \: shorter \: path,  \: A_1=l_1×b_1}$

$\tt\implies \:A_1 \: = 300 \times 5$

$\tt\implies \: \boxed{ \red{ \bf \: A_1 = 1500 \: {m}^{2} }}$

$\tt \pink{Area \: of \: longer \: path, \:  A_2=l_2×b_2}$

$\tt\implies \:A_2 \: = \: 700 \times 5$

$\tt\implies \: \boxed{ \red{ \bf \: A_2 = 3500 \: {m}^{2} }}$

$\tt \blue{Thus, Area \: of \: roads, A_3=A_1+A_2−Area \: of \: common \: path}$

$\tt\implies \:A_3 \: = \: 3500 + 1500 - 5 \times 5$

$\tt\implies \:A_3 = 5000 - 25$

$\tt\implies \: \boxed{ \red{ \bf \: A_3 = 4975 \: {m}^{2} }}$

$\tt \green{Now, \: cost \: of \: constructing \: the \: roads \: }$

$\tt\implies \: cost \: of \: constructing \: roads \: = 4975 \times 105$

$\tt\implies \: \boxed{ \red{ \bf \: \: Cost = Rs \: 522375}}$