Question

If the side of an equilateral ∆PQR is 8 cm,then what is the height of triangle?

Answer 1

Answer:

ANSWER IS IN THE ATTACHMENT

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Answer 2

The height of triangle is $4\sqrt{3}\text{ cm .}$

Explanation:

The area of equilateral triangle = $\dfrac{\sqrt{3}}{4}(side)^2$

If the side of an equilateral ∆PQR is 8 cm , then area of ∆PQR = $\dfrac{\sqrt{3}}{4}(8)^2=\dfrac{\sqrt{3}}{4}(64)=16\sqrt{3}\text{ cm}$  (1)

Also, area of triangle = (0.5) x (base) x (height) =(0.5)(8)(height)= (4)(height)         (2)

From (1) and (2) ,  we have

$(4)(height) = 16\sqrt{3}\\\\\Rightarrow\ height=4\sqrt{3}$

Hence, the height of triangle is $4\sqrt{3}\text{ cm .}$

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