Question

A Triangular Park ABC has sides 120 m, 80m and 50m. a gardener has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of of Rs. 20 per metre leaving a space 3m wide for a gate on one side?​

Answer 1

The perimeter = sum of all sides

= 120 + 80 + 50

= 250

So 250 - 3

247

Left space for gate

Now cost of fencing = Rs 20/per meter

= 247 × 20

= Rs 4,940

Now the area of the triangular park can be found using heron's formula

S = (a+b+c)/2

S = (120+80+50)/2

S = 250/2

S = 125

Now

Herons formula = √s(s-a)(s-b)(s-c)

√125(125-120)(125-80)(120-50)

√125(5)(45)(70)

√5×5×5×5×5×3×3×5×14

After Making pairs

5×5×5×3√14

375√14

Therefore 375√14m is the area of the triangular park

Must click thanks and mark brainliest

Answer 2

$\sf\underline\bold{Answer:}$

• $\sf\small\underline{\underline{Area\: planted\: by\: the\: gardener : 1452.36m^2}}$

• $\sf\small\underline{\underline{The\:cost\:of\:fencing\:the\:park:Rs.4940}}$

$\space$

$\sf\underline\bold{Step-by-Step:}$

$\space$

$\sf\bold{Given(In \:the\:Q):}$

• Sides of the triangular park are 120m,80m and 50m.

$\space$

$\sf\bold{To \: find:}$

• How much area of the park does she need to plant?
• The cost of fencing the park ?

$\space$

$\sf\small{☆Area\:to\:be\:planted=Area \: of \: ∆ABC}$

$\space$

$\sf\underline\bold{Calculating\:area\:of\:∆ABC:}$

$\space$

Use heron's formula to find the area of the triangle.

$\space$

$\mapsto$ $\sf\small{Heron's\:formula=}$

$\sf\sqrt{s(s-a)(s-b)(s-c)}$

• $\sf{Where\:s=semi\:perimeter}$
• $\sf{a,b,c\: = side\:of\:the\:∆}$
• $\sf\small{Here\:a=120,b=80 \:and\: c=50}$

$\space$

$\sf\bold{Now,find\:semi\:parameter:-}$

$\sf\small{Perimeter\:of\:the\:∆=120+80+50=250}$

$\sf\small{Semi-Perimeter:}$ $\sf\dfrac{250}{2}$ $\sf\small{=125m}$

$\space$

$\sf\small{Substitute \: the\:values\:in\:heron's\:formula:}$

$\sf{Area\:of\:the\:∆:-}$

$\mapsto$ $\sf\sqrt{125(125-120)(125-80)(125-50)}$

$\space$

$\mapsto$ $\sf\sqrt{125\times(5)\times(45)\times(75)}$

$\space$

$\mapsto$ $\sf\small\sqrt{2109375}$ $\sf\small{=375}$ $\sf\small\sqrt{15}$

$\space$

$\longmapsto$ $\sf\underline\bold\purple{1452.56m^2}$

______________________________

$\sf\underline\bold{Now,find\:the\:cost\:of\:fencing:}$

$\sf{Cost\:of\:fencing-}$

• $\sf{Rate = Rs.20 per \:meter}$
• $\sf{Left\:space=3m}$

$\space$

$\sf\underline{Hence,the\:gardener\:has\:to\:fence:}$

• $\sf{= 250-3=247m.}$

$\space$

So,total cost of fencing at the rate of Rs.20 per m:-

• $\sf\underline\bold\purple{=247\times20=4940}$

___________________________________