Question

The sides of a triangular field are in the ratio 4 : 5 : 7 , if the perimeter is 32 m . Find the area and cost of leveling at the rate of Rs. per sq,m​

Answer 1

Answer:

I have solve the problem. Hope it helps.

Answer 2

$\huge\rm\underline\blue{GIVEN:}$

• $\large\rm{Ratio\:of\:Sides\:of\:Triangle\:are\:4:5:7}$
• $\large\rm{Perimeter\:of\:triangle\:=\:32m}$

$\huge\rm\underline\blue{TO\:FIND:}$

• $\large\rm{Area\:and\:cost\:of\:levelling\:at\:the\:rate\:of\:Rs.12\:per\:m^2}$

$\huge\rm\underline\blue{SOLUTION:}$

$\large\rm{Let\:The\:Sides\:of\:triangle\:be\:4x,5x\:and\:7x}$

$\large\rm\bold{\boxed{Perimeter\:of\:triangle\:=\:a+b+c}}$

$\large\rm{a,b,c\rightarrow{Sides\:of\:triangle}}$

$\large\rm{\implies{4x+5x+7x\:=\:32}}$

$\large\rm{\implies{16x\:=\:32}}$

$\large\rm{\implies{x\:=\:\frac{32}{16}}}$

$\large\rm{\implies{x\:=\:2}}$

$\large\rm{4x\:=\:4(2)\:=\:8m}$

$\large\rm{5x\:=\:5(2)\:=\:10m}$

$\large\rm{7x\:=\:7(2)\:=\:14m}$

$\large\rm{\therefore{The\:sides\:of\:triangle\:are\:8m,10m,14m}}$

$\large\rm\bold{\boxed{Area\:of\:triangle\:=\:\sqrt{s(s-a)(s-b)(s-c)}}}$

$\large\rm{s\rightarrow{Semiperimeter\:=\:\frac{a+b+c}{2}}}$

$\large\rm{a,b,c\rightarrow{Sides\:of\:triangle}}$

$\large\rm{Semiperimeter\:=\:\frac{8+10+14}{2}}$

$\large\rm{\implies{Semiperimeter\:=\:\frac{32}{2}}}$

$\large\rm{\therefore{Semiperimeter\:=\:16m}}$

$\large\rm{Area\:of\:triangle\:=\:\sqrt{16(16-8)(16-10)(16-14)}}$

$\large\rm{Area\:of\:triangle\:=\:\sqrt{16(8)(6)(2)}}$

$\large\rm{Area\:of\:triangle\:=\:\sqrt{1536}}$

$\large\rm{\therefore{Area\:of\:triangle\:=\:16\sqrt{6}m^2\:=\:16(2.44)\:=\:39.04m^2}}$

$\large\rm{By\:unitary\:method,}$

$\large\rm{per\:m^2\rightarrow{Rs.12}}$

$\large\rm{16\sqrt{6}\rightarrow{'a'}}$

$\large\rm{\implies{a\:=\:12(16\sqrt{6})}}$

$\large\rm{\implies{a\:=\:192\sqrt{6}}}$

$\large\rm{\implies{a\:=\:Rs.192\sqrt{6}\:=\:192(2.44)}}$

$\large\rm{\implies{a\:=\:Rs.468.48}}$

$\large\rm{\therefore{Cost\:of\:levelling\:at\:the\:rate\:of\:Rs.12\:per\:m^2\:is\:Rs.468.48}}$

$\huge\rm\underline\blue{NOTE:}$

$\large\rm{\sqrt{6}\:=\:2.44}$