Question

Find the area of triangle when sides are 18 m , 24 m , 30 m. Find the cost of levelling at the rate of Rs.8 per m^2.​

Answer 1

Given :

• Sides of a triangle are 18 m , 24 m and 30 m.

To Find :

• Area of triangle and cost of levelling at the rate of Rs.8 per m²

Solution :

Let the sides of triangle be " a " , " b " and " c ". Such that a = 18 m , b = 24 m and c = 30 m.

Now area of triangle when sides are given is calculated by ,

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

Where , s is semiperimeter. Semiperimter is calculated by ,

$\\ : \implies \sf \: s = \frac{a + b + c}{2}$

By substituting the values we have we get ;

$\\ : \implies \sf \: s = \frac{18 + 24 + 30}{2}$

$\\ : \implies \sf \: s = \frac{72}{2}$

$\\ : \implies\underline{\boxed{\sf{ \: s = 36 \: m}}}$

By substituting the value of semiperimeter in Heron's formulae we get ;

$\\ : \implies \sf \: a = \sqrt{36(36 - 18)(36 - 24)(36 - 30)}$

$\\ : \implies \sf \: a = \sqrt{36(18)(12)(6)}$

$\\ : \implies \sf \:a = \sqrt{46656}$

$\\ : \implies\underline{\boxed{\sf {\: a = 216 \: m {}^{2} }}}$

Now , We are given that cost of levelling per m² is Rs.8

Then cost of levelling per 216 m² is , Rs. 216 × 8 = Rs.1728

Hence , The total cost of levelling is Rs.1728.

Answer 2

Given :

Sides of triangle :

• a = 18

• b =24

• c = 30

To Find :

1. Find the area of triangle
2. Find the cost of levelling at the rate of Rs.8 per m^2.

Solution :

To calculate the area of given triangle we will use the heron's formula :

$: \implies \: \: \: \: \:\boxed{ \sf \: s = \frac{a+b+c}{2}} \:$

Substitute all values :

$: \implies \: \: \: \: \:\sf \: s = \frac{18+24+30}{2} \: \\ \\ \\ : \implies \: \: \: \: \:\sf \: s = \cancel{\frac{72}{2}} \: \\ \\ \\ : \implies \: \: \: \: \:\sf \: s = 36$

$: \implies \: \: \: \: \: \boxed{ \sf \red{Area = \sqrt{s(s-a)(s-b)(s-c)}}}$

Substitute all values

$: \implies \sf\: \: \: \: \:Area = \sqrt{36(36-18)(36-24)(36-30)} \\ \\ \\ \: : \implies \sf\: \: \: \: \:Area =\sqrt{36 \times 18 \times 12 \times 6} \\ \\ \\ : \implies \sf\: \: \: \: \:Area =\sqrt{46656} \: \\ \\ \\ : \implies \sf\: \: \: \: \orange{Area = 216 } \: {m}^{2}$

Hence the area of the triangle is 216 m² meters

Find the cost of levelling at the rate of Rs.8 per m^2.

$: \implies \sf \: \: \: \: \: \: 216 \times 8 \\ \\ \\ : \implies \sf \: \: \: \: \:1728 \: rupees$

The cost of leveling is 1728 RS.