Question

A triangular park abc has sides 12m, 8 m, and 50 m. a gardener wants to put a fence all around it and also plant grass inside. how much area does he need to plant? find the cost of fencing it with barbed wire at the rate of rs 80 per metre leaving a space 3 m wide for a gate on one side

Answer 1

GIVEN ✅

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

perimeter of the triangular park = 120m + 80m + 50m

= 250m

therefore it's semi-perimeter = 250/2

= 125m

$\begin{gathered}\tt \small \: area \: of \: the \: triangular \: park \: by \\ \tt \small herons \: formula = \scriptsize {\sqrt{s(s - a)(s - b)(s - c)} } \\ \tt \footnotesize = \sqrt{125(125 - 120)(125 - 80)(125 - 50)} \\ \tt \footnotesize = \sqrt{125 \times 5 \times 45 \times 75} \\ \tt \footnotesize = \sqrt{2109375} \\ \tt \small = 1452.36 {m}^{2} \: \end{gathered}$

hence, the gardener have to plant grass in 1452.36m²

now we have to find the cost of fencing the field with a barbed wire at the rate of rs 20 per m leaving a space of 3m wide for a gate.

therefore the gardener have to fence = 250 - 3

= 247m

so total cost of fencing at the rate of rs 20 per meter = 247 × 20

= rs 4940

$\huge\sf \underline {\red {hope \: its \: helping \: you \: }}$