Perimeter of a square and an equilateral tria | vedclass

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

Question

(A) For a square,the diagonal is given by $d = a \sqrt{2}$,where $a$ is the side length.Given $d = 12 \sqrt{2} 	ext{ cm}$,so $a = 12 	ext{ cm}$.The

Vedclass · Accepted Answer

$64 \sqrt{3} 	ext{ cm}^2$

Vedclass · Answer

(A) For a square,the diagonal is given by $d = a \sqrt{2}$,where $a$ is the side length.Given $d = 12 \sqrt{2} 	ext{ cm}$,so $a = 12 	ext{ cm}$.The perimeter of the square is $P = 4a = 4 	imes 12 = 48 	ext{ cm}$.Since the perimeter of the equilateral triangle is equal to the perimeter of the square,the perimeter of the triangle is $48 	ext{ cm}$.Let the side of the equilateral triangle be $s$. Then $3s = 48 	ext{ cm}$,which gives $s = 16 	ext{ cm}$.The area of an equilateral triangle is given by $\frac{\sqrt{3}}{4} s^2$.Area $= \frac{\sqrt{3}}{4} 	imes (16)^2 = \frac{\sqrt{3}}{4} 	imes 256 = 64 \sqrt{3} 	ext{ cm}^2$.

Perimeter of a square and an equilateral triangle is equal. If the diagonal of the square is $12 \sqrt{2} \text{ cm}$,then find the area of the equilateral triangle.

Similar Questions

The area of a circle is $154 \, cm^{2}$. The length of an arc of the circle which subtends an angle of $45^{\circ}$ at the centre is......$cm$.

$A$ lawn in the form of a rectangle has a length twice its width. The area of the lawn is $\frac{2}{3}$ hectares. The length of the lawn is:

The sides of a triangle are in the ratio $\frac{1}{4}: \frac{1}{6}: \frac{1}{8}$ and its perimeter is $91\, cm$. The difference of the length of the longest side and that of the shortest side is

The perimeter of a rhombus is $60 \, cm$ and one of its diagonals is $24 \, cm$. The area (in $sq. cm$) of the rhombus is

The diagonals of a rhombus are $12 \ cm$ and $16 \ cm$. The length of one side is.......$cm$

Vedclass Test Series

Exam Paper Generator

Online Exam Module