Question

The perimeter of an equilateral triangle is 21 inches. Find the length of the altitude

Answer 1

an equilateral triangle has all equal sides, thus EQUI = equal.

so 21 ÷ 3 = 7, so each side is 7, 7+7+7 = 21 <- perimeter.

$\bf \textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=length~of\\ \qquad a~side\\[-0.5em] \hrulefill\\ s=7 \end{cases}\implies h=\cfrac{7\sqrt{3}}{2}\implies h\approx 6.06$

Answer 2

We began by splitting the triangle to form a right triangle, then we found the height using the SOH CAH TOA rule as 6 inches

Given data

• Perimeter of equilateral triangle = 21 inches

Since the sides of the equilateral triangle is equal, each side will be

= 21/3

= 7 inches

We can form a right angled triangle by dividing the triangle into two halves, hence the base of the 7/2 = 3.5 inches

The angle of two sides of right angled triangle is 45 degrees

Hence applying SOH CAH TOA we have

Sin Ф = opp/Hyp

Sin 45 = opp/7

0.8509 = opp/7

cross multiplying we have

opp = 0.8509*7

opp = 5.95

Hence the height is Approx 6 inches

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