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

Write True or False and justify your answer.
In a triangle,the sides are given as $11 \, cm$,$12 \, cm$,and $13 \, cm$. The length of the altitude corresponding to the side of length $12 \, cm$ is $10.25 \, cm$.

For a rhombus plot,its perimeter is $680 \, m$ and one of its diagonals is $300 \, m$. Find the area of the plot. (in $, m^2$)

In the figure,$\Delta ABC$ has sides $AB = 7.5\, cm$,$AC = 6.5\, cm$,and $BC = 7\, cm$. On base $BC$,a parallelogram $DBCE$ of the same area as that of $\Delta ABC$ is constructed. Find the height $DF$ of the parallelogram (in $cm$).

The perimeter of an isosceles triangle is $32 \, cm$. The ratio of the equal side to its base is $3:2$. Find the area of the triangle.

$A$ field in the form of a parallelogram has sides $60 \, m$ and $40 \, m$ and one of its diagonals is $80 \, m$ long. Find the area of the parallelogram.

Vedclass Test Series

Exam Paper Generator

Online Exam Module