Question

a square and an equivalent triangle triangle have equal perimeter .If the diagonal of the square is 12√2cm then find area of triangle​

Answer 1

Answer:

64√3 cm

Given:

A square ABCD and an equilateral traingle have equal perimeter

And diagonal of square us 12√2 cm

To find:

Area of Triangle

Solution:-

Diagonal of square=12√2 cm

We know that

$diagnal \: of \: square \: = \sqrt{2}a$

$12 \sqrt{2} = \sqrt{2}a$

$\frac{ 12\sqrt{2} }{2} = a$

$12 = a$

Side of square=12 cm

Then perimeter of square=4(side)

=4×12

=48 cm

Let sides of equilateral traingle be x

Then it will be 3x

According to the question

perimeter of square=perimeter of equilateral triangle

48=3x

48/3=x

X=16

$area \: of \: triangle = \frac{ \sqrt{3} }{4} {(side)}^{2}$

$= \frac{ \sqrt{3} }{4} \times 16 \times 16$

$= 64 \sqrt{3} \: cm$

---------------------

Area of triangle is 64√3 cm

Answer 2

Answer:

${\sf{\therefore Area\:of\:triangle=110.72cm^{2}}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about diagonal of square and perimeter of square is equal to perimeter of equilateral triangle.

• We have to find the area of triangle.

$\underline \bold{Given : } \\ \implies Diagonal \: of \: square = 12 \sqrt{2} \: cm \\ \implies Perimeter \: of \: square = Perimeter \: of \:equilateral \: triangle \\ \\ \underline \bold{To \: Find : } \\ \implies Area \: of \: triangle = ?$

• According to given question :

$\bold{ In \: Diagonal \: of \: square}\\ \implies Diagonal \: of \: square = \sqrt{2} a \\ \implies 12 \sqrt{2} = \sqrt{2} a \\ \implies a = \frac{12 \sqrt{2} }{ \sqrt{2} } \\ \bold {\implies a = 12 \: cm} \\ \\ \implies Perimeter \: of \: square = 4a \\ \implies Perimeter = 4 \times 12 \\ \bold{\implies Perimeter = 48 {cm}} \\ \\ \bold{Let \: side \: of \: equilateral \: triangle = x}\\ \implies Perimeter \: of \: triangle = a + b + c \\ \implies 48 {cm} = 3x \\ \implies x = \frac{48}{3} \\ \bold {\implies x = 16} \\ \\ \implies Area \: of \: triangle = \frac{ \sqrt{3} {a}^{2} }{4} \\ \implies Area = \frac{ \sqrt{3} \times 16 \times 16 }{4} \\ \implies Area = 64 \sqrt{3} \\ (\bold{as \: \sqrt{3} = 1.73}) \\ \implies Area = 64 \times 1.73 \\ \bold{\implies Area = 110.72 {cm}^{2} } \\ \\ \bold{\therefore Area \: of \: triangle = 110.72 {cm}^{2} }$