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

Among a square of perimeter $44\, cm$ and a circle of circumference $44\, cm,$ which figure has a larger area and by how much?

The minute-hand of a clock is $14 \, cm$ long. The area covered by the minute hand in $30 \, min$ is.............$cm^2$

The sides of a right-angled triangle forming the right angle are in the ratio $5: 12$. If the area of the triangle is $270 \, cm^2$,then the length of the hypotenuse is .......... $cm$.

The percentage increase in the area of a rectangle,if each of its sides is increased by $20 \%$,is.........$\%$

$A$ bed of roses is shaped as shown in the figure below. In the centre is a square and on each side there is a semi-circle. The side of the square is $21 \, m$. If each rose plant needs $6 \, m^{2}$ of space,then the number of plants in the bed is?

Vedclass Test Series

Exam Paper Generator

Online Exam Module