The perimeter of an isosceles triangle is 32 | vedclass

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

Question

(C) Let the equal sides be $3x$ and the base be $2x$.The perimeter of the triangle is the sum of all sides: $3x + 3x + 2x = 32 \, cm$.$8x = 32 \implie

Vedclass · Accepted Answer

$32 \sqrt{2} \, cm^2$

Vedclass · Answer

(C) Let the equal sides be $3x$ and the base be $2x$.The perimeter of the triangle is the sum of all sides: $3x + 3x + 2x = 32 \, cm$.$8x = 32 \implies x = 4$.Thus,the sides are $a = 12 \, cm$,$b = 12 \, cm$,and $c = 8 \, cm$.The semi-perimeter $s = \frac{32}{2} = 16 \, cm$.Using Heron's formula,Area $= \sqrt{s(s-a)(s-b)(s-c)}$.Area $= \sqrt{16(16-12)(16-12)(16-8)} = \sqrt{16 	imes 4 	imes 4 	imes 8}$.Area $= \sqrt{16 	imes 16 	imes 8} = 16 	imes 2\sqrt{2} = 32\sqrt{2} \, cm^2$.

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.

Similar Questions

Find the area of the triangular field with the length of the sides $360 \, m$,$450 \, m$,and $450 \, m$.

In quadrilateral $ABCD$, $\angle A = 90^{\circ}$, $AB = 15 \text{ cm}$, $BC = 25 \text{ cm}$, $CD = 12 \text{ cm}$, and $DA = 8 \text{ cm}$. Find the area of quadrilateral $ABCD$. (in $\text{ cm}^2$)

An isosceles triangle has a perimeter of $50\,cm$ and each of the equal sides is $17\,cm$. Find the area of the triangle. (in $,cm^2$)

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 $10.25 \, cm$.

The area of an isosceles triangle having base $2 \, cm$ and the length of one of the equal sides $4 \, cm$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module