Question

Find the cost of levelling the ground in the form of triangle having sides 17 m , 12 m, and 25 m at the rate of rupee 3 per sq. m​

Answer 1

Given :

• 1st side of a triangle is 17 m
• 2nd side of a triangle is 12 m
• 3rd side of a triangle is 25 m

To find :

• Cost of leveling

According to the question,

In this at first we have to find the area of triangle by using Heron's formula then we will multiply the area by 3.

$\sf\red {Heron's\: formula : \: \sqrt{s(s - a)(s - b)(s - c)} }$

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

$\dashrightarrow\sf{s = \frac{17 + 12 + 25}{2} }$

$\dashrightarrow\sf{s = \cancel\frac{54}{2} = 27 \: m} \green \bigstar$

$\dashrightarrow \sf{ \sqrt{27(27 - 17)(27 - 12)(27 - 25)} }$

$\dashrightarrow\sf{ \sqrt{27(10)(15)(2)} }$

$\dashrightarrow\sf{ \sqrt{3 \times 3 \times 3 \times 5 \times 2 \times 5 \times 3 \times 2} }$

$\dashrightarrow\sf{3 \times 3 \times 5 \times 2}$

$\dashrightarrow\sf{ {90 \: m}^{2}\orange\bigstar}$

Now we will find cost of leveling the ground,

$\dashrightarrow \sf{90 \times 3}$

So,the cost of leveling is ₹ 270...

Answer 2

Given :-

• sides of a triangle are 17 m , 12 m, and 25 m .

To find :-

• Cost of leveling at the rate of rupee 3 per sq. m

Solution:-

We know,

$\sf\underline{\boxed{\pink {✷Heron's\: formula : \: \sqrt{s(s - a)(s - b)(s - c)}}}}$

$\sf Where, \orange{✷S =a + b+c /2}$

And , a , b , c are sides of the triangle .

$\implies \sf{s = \frac{17 + 12 + 25}{2} }\\ \\ </p><p>\implies s = \cancel\frac{54}{2} = 27 \: m$

$\implies \sf{ \sqrt{27(27 - 17)(27 - 12)(27 - 25)} }\\ \\ \\</p><p>\implies \sf{ \sqrt{27(10)(15)(2)} }\\ \\ \\ </p><p>\implies \sf{ \sqrt{3 \times 3 \times 3 \times 5 \times 2 \times 5 \times 3 \times 2} }$

$\implies \sf{3 \times 3 \times 5 \times 2}$

$\dashrightarrow\sf{ {90 \: m}^{2}}$

Now , cost of leveling the ground :-

$\implies \sf{90 \times 3}$

Hence, $\underline{\pink{\boxed{Cost\: of\: leveling = Rs.270}}}$

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