Question

A rectangular field is 125m long and 75m wide. Two cross roads, each of width 5m, cut at right angles through the centre of the field. Find the area of the roads. Also, find the cost of planting trees in the remaining field at the rate of 350 per sq m

Answer 1

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Answer 2

$\underline {\blue { Dimensions \:of \:a \: rectangular \:field(ABCD) :}}$

$Length (AB) = 125 \: m , \: Breadth (BC)= 75 \:m$

$\pink { Width \:of \:a \:path = 5 \:m }$

$\underline {\blue { Dimensions \:of \:a \: rectangle (PQRS) :}}$

$Length (PQ) = 125 \: m , \: Breadth (PS)= 5 \:m$

$\underline {\blue { Dimensions \:of \:a \: rectangle (KLMN) :}}$

$Length (KN) = 75 \: m , \: Breadth (KL)= 5 \:m$

$\underline {\blue { Dimensions \:of \:a \: Square(EFGH) :}}$

$Side (EF) = 5 \:m$

$\underline {\red { Area \:of \:the \:Roads:}}$

$A_{(1)} = Area (PQRS )+ Area (KLMN) - Area (EFGH )$

$\implies A = PQ \times PS + KN \times KL - EF^{2} \\= 125 \times 5 + 75 \times 5 - 5^{2} \\= 625 + 375 - 25 \\= 975 \:m^{2}\: --(1)$

$ii) Area \: of \:the \: Remaining \: field \\= Area (ABCD) - Area \:of \:cross \:roads$

$= AB \times BC - (1) \\= 125 \: m \times 75 \:m - 975 \:m^{2} \\= 9375 \:m^{2} - 975 \:m^{2} \\= 8400 \:m^{2}\: --(2)$

$iii ) Cost \: of \: planting \: trees \:in \:the \\</p><p>remaining \:1 \: square \:metre \: field = Rs \: 350$

$Cost \: of \: planting \: trees \:in \:the \\</p><p>remaining \:8400 \: square \: metres \: field \\= 350 \times 8400 \\= Rs \: 2940 000$

Therefore.,

$\red {Area \:of \:the \:Roads} \green {= 975 \:m^{2}}$

$\red{ Cost \: of\:planting \:trees }\green {= Rs \: 2940 000}$

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