Find the area of a triangular field,two sides | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the sides of the triangle be $a = 510\,m$,$b = 520\,m$,and $c$. The perimeter $P = a + b + c = 1560\,m$. $510 + 520 + c = 1560 \implies 1030 +

Vedclass · Accepted Answer

$1,17,000\,m^2$,Rs. $24,57,000$

Vedclass · Answer

(C) Let the sides of the triangle be $a = 510\,m$,$b = 520\,m$,and $c$. The perimeter $P = a + b + c = 1560\,m$. $510 + 520 + c = 1560 \implies 1030 + c = 1560 \implies c = 530\,m$. The semi-perimeter $s = P/2 = 1560/2 = 780\,m$. Using Heron's Formula,Area $= \sqrt{s(s-a)(s-b)(s-c)}$. Area $= \sqrt{780(780-510)(780-520)(780-530)} = \sqrt{780 	imes 270 	imes 260 	imes 250}$. Area $= \sqrt{(78 	imes 10) 	imes (27 	imes 10) 	imes (26 	imes 10) 	imes (25 	imes 10)} = \sqrt{78 	imes 27 	imes 26 	imes 25 	imes 10^4}$. Area $= \sqrt{(3 	imes 26) 	imes (27) 	imes (26) 	imes (25) 	imes 10^4} = \sqrt{26^2 	imes 81 	imes 25 	imes 10^4} = 26 	imes 9 	imes 5 	imes 100 = 1,17,000\,m^2$. Cost $= 	ext{Area} 	imes 	ext{Rate} = 1,17,000 	imes 21 = 	ext{Rs. } 24,57,000$.

Find the area of a triangular field,two sides of which are $510\,m$ and $520\,m$ and the perimeter is $1560\,m$. Also,find the cost of the field at the rate of Rs. $21$ per $m^2$.

Similar Questions

$A$ rhombus-shaped sheet with a perimeter of $40 \, cm$ and one diagonal of $12 \, cm$ is printed on both sides at the rate of $Rs. \, 5$ per $cm^2$. Find the total cost of printing.

Write True or False and justify your answer.
The cost of levelling the ground in the form of a triangle having the sides $51 \, m$,$37 \, m$,and $20 \, m$ at the rate of $Rs \, 3$ per $m^2$ is $Rs \, 918$.

In $\Delta ABC$,$AB = 20 \, cm$,$BC = 48 \, cm$,and $AC = 52 \, cm$,find the area of $\Delta ABC$. (in $, cm^2$)

Write True or False and justify your answer.
The base and the corresponding altitude of a parallelogram are $10 \text{ cm}$ and $3.5 \text{ cm}$,respectively. The area of the parallelogram is $30 \text{ cm}^2$.

Area of a rhombus $=$ ............

Vedclass Test Series

Exam Paper Generator

Online Exam Module