Question

Find the height of an equilateral triangle having side 15 cm

Answer 1

given :-

side of the equilateral triangle = 15cm

formula to find area of an equilateral triangle is √3side²/4

it's area = √3side²/4

= (√3 × 15 × 15)/4

= 225√3/4cm²

also we know that formula to find the area of a triangle is 1/2 × b × h where b is the side of the equilateral triangle.

➡ 1/2 × b × h = 225√3/4cm²

➡ 1/2 × 15 × h = 225√3/4cm²

➡ 15 × h = 225√3/4 × 2

➡ 15 × h = 225√3/2

➡ h = 225√3/2 × 1/15

➡ h = 15√3/2cm

hence, the height of the equilateral triangle is 15√3/2cm or 7.5√3cm

Answer 2

$\huge\pink{ANSWER:-}$

The side of the equilateral Triangle is

$\frac{ \sqrt{3} }{4} {a }^{2} \\ \\ here \: a \: is \: 15cm \\ \\ \frac{ \sqrt{3} }{4} \times {15}^{2} \\ \\ = \frac{225 \sqrt{3} }{4} {cm}^{2} \\ \\ hence \: we \: know \: that \: formula \: of \\ \: triangle \: is \\ \\ \frac{1}{2} \times b \times h \\ \\ = \frac{225 \sqrt{3} }{4} = \frac{1}{2} \times 15 \times h \\ \\ = h = \frac{225 \sqrt{3} }{4} \times 2 \times \frac{1}{15} \\ \\ = h = \frac{15 \sqrt{3} }{2}$