Question

A square and an equilateral triangle have equal perimeter.if the diagonal of the square is 12 root 5 find the area of the triangle

Answer 1

Answer:

area of triangle is 134

Answer 2

$\huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

$\Large{\underline{\bf{Given :}}}$

Diaginal of the square is 12√5 units.

Perimeter of square and equilateral triangle are equal.

$\rule{200}{2}$

$\Large{\underline{\bf{To \: Find:}}}$

We have to find the area of the equilateral triangle.

$\rule{200}{2}$

$\Large{\underline{\bf{Solution :}}}$

We know the formula to find the Diagonal of square.

$\large{\star{\underline{\boxed{\sf{Diagonal = \sqrt{2} \times a}}}}}$

12√5 = √2 * a

(12√5)/√2 = a

Side = 19 unit (approx)

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Now, we will find Perimeter of square.

$\large{\star{\underline{\boxed{\sf{Perimeter = 4 \times side}}}}}$

Perimeter = 4 * 19

Perimeter = 76 units.

$\large{\star{\underline{\boxed{\sf{Perimeter = 76 \: units}}}}}$

$\rule{200}{2}$

Now,

We will find perimeter of the equilateral Triangle.

$\large{\star{\underline{\boxed{\sf{Perimeter = 3 \times a}}}}}$

Where, a is the side of equilateral triangle.

76 = 3 * a

76/3 = a

a = 25.34 unit

Hence, side of the equilateral triangle is 25.34

$\large{\star{\underline{\boxed{\sf{Side = 25.34 \: units}}}}}$

$\rule{200}{2}$

Now, we will find area of the equilateral triangle.

$\large{\star{\underline{\boxed{\sf{Area = \frac{\sqrt{3}}{4} \times a^2}}}}}$

$\sf{area = \frac{ \sqrt{3} }{4} \times {(25.34)}^{2} } \\ \\ \sf{area = \frac{ \sqrt{3} }{4} \times 642.1156 } \\ \\ \sf{area = \sqrt{3} \times 160.5289 } \\ \\ \sf{area = 280.04 \: unis }$

$\large{\star{\underline{\boxed{\sf{Area = 280.04 \: units }}}}}$