Question

question 6 (1 point) an equilateral triangle has a side length of 7 cm. if a perpendicular is dropped from a corner, what is the length of the perpendicular? give the exact value, not an approximation. a) \\( \frac { 7 \sqrt { 3 } } { 2 } \mathrm { cm } \\) b) \\( 7 \sqrt { 3 } \mathrm { cm } \\) c) \\( \sqrt { 3 } \mathrm { cm } \\) d) \\( \frac { \sqrt { 3 } } { 2 } \mathrm { cm } \\)

Explanation:

Step1: Recall the formula for the perpendicular of an equilateral triangle

For an equilateral triangle with side length \(a\), the length of the perpendicular \(h=\frac{\sqrt{3}}{2}a\).

Step2: Substitute the value of \(a = 7\) cm into the formula

Here \(a = 7\) cm. So, \(h=\frac{7\sqrt{3}}{2}\) cm.

Answer:

A. \(\frac{7\sqrt{3}}{2}\) cm