Question

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

Answer 1

Explanation:

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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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✡ VERIFICATION :

From above calculations we have h = 7.5√3

Put value of h in this : $\dfrac{1}{2}$ × 15 × h = $\dfrac{ \sqrt{3} {(15)}^{2} }{4}$

=> $\dfrac{1}{2}$ × 15 × 7.5√3 = $\dfrac{ \sqrt{3} {(15)}^{2} }{4}$

=> 7.5 × 7.5√3 = 56.25√3

=> 56.25√3 = 56.25√3

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