Question

Write True or False and justify your answer :

The cost of levelling the ground in the form of a triangle having sides $51$ m, $37$ m and $20$ m at the rate of Rs $3$ per $m^2$ is Rs $918$

Answer 1

Step 1 : Find the area of triangular ground

Given : Sides of triangular ground are $51$ m, $37$ m and $20$ m

Let $a=51$ m, $b=37$ m and $c=20$ m

$\therefore$ Semi-perimeter $\left(s\right)=\frac{a+b+c}{2}$

$=\frac{51+37+20}{2}$

$=\frac{108}{2}$

$=54$

$\therefore$ Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{54(54-51)(54-37)(54-20)}$

$=\sqrt{54\left(3\right)\left(17\right)\left(34\right)}$

$=\sqrt{9\times 3\times 2\times 3\times 17\times 2\times 17}$

$=3\times 3\times 2\times 17$

$=306{\text{m}}^2$

Step 2 : Find the total cost of levelling

$\because$ Cost of levelling per $m^2=\text{Rs}3$

Cost of levelling $306m^2=\text{Rs}306\times 3$

$=\text{Rs}918$

Thus, total cost of levelling is Rs $918$

Hence, the given statement is true.