Question

what is the height, x, of the equilateral triangle? image of equilateral triangle with base 14 in. and angles 60° each, height labeled x options: a. $7\sqrt{3}$ inches, b. 7 inches, c. $14\sqrt{3}$ inches, d. 14 inches, e. $7\sqrt{2}$ inches

Explanation:

Step1: Divide the equilateral triangle

Divide the equilateral triangle into two right - angled triangles. The base of each right - angled triangle is $\frac{14}{2}=7$ inches. The hypotenuse of the right - angled triangle is 14 inches.

Step2: Apply the Pythagorean theorem

Let the height be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 14\) (hypotenuse) and \(a = 7\) (base of the right - angled triangle), and \(b=x\) (height).

$$x=\sqrt{14^{2}-7^{2}}=\sqrt{(14 + 7)(14 - 7)}=\sqrt{21\times7}=\sqrt{7\times3\times7}=7\sqrt{3}$$

Answer:

A. \(7\sqrt{3}\) inches