An isosceles triangle has a perimeter of 84 , | vedclass

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

Question

(C) Let the equal sides be $a = 30 \, cm$ and $b = 30 \, cm$. Given the perimeter $P = 84 \, cm$,the third side $c$ is calculated as $c = P - (a + b)

Vedclass · Accepted Answer

$72 \sqrt{21} \, cm^2$

Vedclass · Answer

(C) Let the equal sides be $a = 30 \, cm$ and $b = 30 \, cm$. Given the perimeter $P = 84 \, cm$,the third side $c$ is calculated as $c = P - (a + b) = 84 - (30 + 30) = 84 - 60 = 24 \, cm$. The semi-perimeter $s = P / 2 = 84 / 2 = 42 \, cm$. Using Heron's formula,the area $A = \sqrt{s(s-a)(s-b)(s-c)}$. $A = \sqrt{42(42-30)(42-30)(42-24)}$. $A = \sqrt{42 	imes 12 	imes 12 	imes 18}$. $A = 12 \sqrt{42 	imes 18} = 12 \sqrt{756}$. Since $756 = 36 	imes 21$,we have $A = 12 	imes 6 \sqrt{21} = 72 \sqrt{21} \, cm^2$.

An isosceles triangle has a perimeter of $84 \, cm$ and each of the equal sides is $30 \, cm$. Find the area of the triangle.

Similar Questions

In quadrilateral $ABCD$,$AB = 9 \, cm$,$BC = 13 \, cm$,$CD = 14 \, cm$,$DA = 12 \, cm$,and $BD = 15 \, cm$. Find the area of quadrilateral $ABCD$ in $cm^2$.

Write True or False and justify your answer.
The area of the isosceles triangle is $\frac{5}{4} \sqrt{11} \, cm^2$,if the perimeter is $11 \, cm$ and the base is $5 \, cm$.

If each side of a triangle is doubled,then find the ratio of the area of the new triangle thus formed to the area of the given triangle.

The sides of a triangle measure $15 \text{ cm}$,$17 \text{ cm}$,and $20 \text{ cm}$. Then,the semi-perimeter of the triangle is ......... $\text{cm}$.

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 $m^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module