Question

the lenfth of each side of an quadilatrial triangle having an area of 25route3​

Answer 1

Given :

• Area of equilateral triangle is 25√3

To Find :

• Length

According to the question,

$\bigstar \: \purple {\boxed{ \sf {Area \: of \: equilateral _{ \triangle } = \dfrac{ \sqrt{3} }{4} \times {(side)}^{2} }}}$

Putting the value according to the formula,

$\: \: \: \: \: \: \: \: \: \implies \sf{ \dfrac {\cancel { \sqrt{3}} }{4} \times (Side) {}^{2} = 25 \cancel{\sqrt {3}} }\\ \\ \: \implies \sf{ \frac{1}{4} \times ( {Side)}^{2} = 25 }\\ \\ \:\implies \sf{( {Side)}^{2} = 25 \times 4} \\ \\\implies\sf{{(Side)}^{2} = 100 } \\ \\ \implies\sf \: Side = \sqrt{100} \\ \\\sf\therefore {\boxed {\sf \red{Side \: = 10 \: cm}}}$

So,the side is 10 cm..

__________...

More formulas :

$\bullet \sf{ \: Area \: of \: _{ \triangle} = \sqrt{s(s - a)(s - b)(s - c)} }$

$\bullet \: \sf{Area \: of \: reactangle = length \times breadth}$

$\bullet\sf{ \: Area \: of \: square = side \times side}$

$\bullet \: \sf{Perimeter \: of \: _{ \triangle} = sum \: of \: all \: its \: side }$

$\bullet\sf{Perimeter \: of \: rectangle =2(length + breadth }$

Answer 2

Given: Area of the equilateral triangle = 25√3 cm²

To Find: Length of each side of the triangle.

We know,

area of an equilateral triangle = (√3)/4 s²

where, s is the length of one side of the triangle.

Let the side be = s

∴ (√3)/4 s² = 25√3

→ s² = 25√3 × 4/√3

→ s² = 25 × 4

→ s = √(25 × 4)

→ s = 5 × 2 = 10 cm

s = 5 × 2 = 10 cm

∴ Length of a side of the triangle is 10 cm.