Question

Find the height of equilateral triangle whose side is 15 cm​

Answer 1

ANSWER :-

$area \: \: of \: \: triangle = \frac{ \sqrt{3 } {a}^{2} }{4} \\ \\ = \frac{ \sqrt{3} }{4} \times 15 \times 15 \\ \\ = \frac{225 \sqrt{3} }{4} \\ \\ we \: \: know \: \: the \: \: area \: of \: \: triangle \: \: \\ \\ = \frac{1}{2} \times b \times h \\ \\ \frac{225 \sqrt{3} }{4} = \frac{1}{2} \times 15 \times h \\ \\ h = \frac{225 \sqrt{3} }{4} \times 2 \times \frac{1}{15} \\ \\ h = \frac{15 \sqrt{3} }{4} \\ \\ h = 7.5 \sqrt{3}$

Answer 2

» Side of equilateral triangle is 15 cm

_____________ [ GIVEN ]

• We have to find the height (h) of the equilateral triangle.

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We know that ..

Area of equilateral triangle = $\dfrac{ \sqrt{3} {a}^{2} }{4}$

And area of triangle = $\dfrac{1}{2}$ × b × h

→ $\dfrac{1}{2}$ × b × h = $\dfrac{ \sqrt{3} {a}^{2} }{4}$

And we have given side of triangle = a = 15 cm. Also base (b) = 15 cm

Put it in above formula

→ $\dfrac{1}{2}$ × 15 × h = $\dfrac{ \sqrt{3} {(15)}^{2} }{4}$

→ h = $\dfrac{ \sqrt{3} \: \times \: 225 \: \times \: 2}{4 \: \times \: 15}$

→ h = $\dfrac{ \sqrt{3} \: \times \:450}{60}$

→ h = $7.5\sqrt{3}$

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$7.5\sqrt{3}$ is the height of the equilateral triangle.

_________ [ ANSWER ]

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