The perimeter of an isosceles triangle is 14 | vedclass

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

Question

(D) Let the lateral sides be $5x$ and the base be $4x$.Since it is an isosceles triangle,the two equal sides are $5x$ and $5x$.The perimeter is the su

Vedclass · Accepted Answer

$2 \sqrt{21}$

Vedclass · Answer

(D) Let the lateral sides be $5x$ and the base be $4x$.Since it is an isosceles triangle,the two equal sides are $5x$ and $5x$.The perimeter is the sum of all sides: $5x + 5x + 4x = 14x$.Given the perimeter is $14 \ cm$,we have $14x = 14$,which gives $x = 1$.Thus,the sides of the triangle are $5 \ cm, 5 \ cm$,and $4 \ cm$.The semi-perimeter $s$ is calculated as $s = \frac{5+5+4}{2} = 7 \ cm$.Using Heron's formula,Area $= \sqrt{s(s-a)(s-b)(s-c)}$.Area $= \sqrt{7(7-5)(7-5)(7-4)} = \sqrt{7 	imes 2 	imes 2 	imes 3}$.Area $= \sqrt{7 	imes 4 	imes 3} = 2 \sqrt{21} \ cm^2$.

The perimeter of an isosceles triangle is $14 \ cm$. The lateral side and the base are in the ratio $5:4$. The area of the triangle in $cm^2$ is:

Similar Questions

The diagonal of a square field measures $50 \, m$. The area of the square field is.........$m^2$?

The volume of a cube is $216 \, cm^3$. Part of this cube is then melted to form a cylinder of length $8 \, cm$. Find the volume of the cylinder (in $cm^3$)?

$A$ wire which when bent in the form of a square encloses an area of $484 \, cm^2$. What will be the enclosed area when the same wire is bent into the form of a circle? (in $cm^2$)

The hypotenuse and the semi-perimeter of a right triangle are $20\, cm$ and $24\, cm$,respectively. The other two sides of the triangle are

Find the perimeter of a circular plot which occupies an area of $154 \, m^{2}$ (in $m$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module