Question

the side of a triangular ground are 5 7 and 8 respectively find the cost of levelling the ground at the rate of rupees 10 per metre square

Answer 1

Answer :

Given sides of triangular ground= 5m, 7m and 8m

So, when the sides of a triangle are given, then its area can be found by using Heron's formula.

Heron's Formula =>

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

where s = semiperimeter (half of Perimeter)

a,b and c are the sides of triangle.

So, let
a = 5m
b = 7m
c = 8m

$= > \: semiperimeter \: (s) = \frac{sum \: of \: sides}{2} \\ \\ semiperimeter \:(s) = \frac{a + b + c}{2} \\ \\ = > s = \frac{5 + 7 + 8}{8} \\ \\ s = \frac{20}{2} \\ \\ s = 10m$
$therefore \\ area \: of \: triangular \: ground \: = > \\ \\ \sqrt{10(10 - 5)(10 - 7)(10 - 8)} \\ \\ = > \sqrt{10 \times 5 \times 3 \times 2} \\ \\ = > \sqrt{300} \\ \\ \sqrt{ {10}^{2} \times 3} \\ \\ \sqrt{ {10}^{2} } \sqrt{3} \\ \\ 10 \sqrt{3} \\ \\ 17.32051 \: m {}^{2}$

$cost \: of \: levelling \: 1 \: {m}^{2} = rs.10 \\ \\ cost \: of \: levelling \: 17.32051 \: {m}^{2} = 10 \times 17.32051 \\ \\ = > rs. \: 173.2051$

HOPE IT WOULD HELP YOU

Answer 2

Step-by-step explanation:

area=square root of s(s-a)(s-b)(s-c)

semi perimeter =5+7+8÷2

=20÷2

=10cm

leveling ground per sq m=

rs 10sq m

10×10=rs .100