Question

select the correct answer.
what is the height, x, of the equilateral triangle?
a. ( 7sqrt{3} ) inches
b. 7 inches
c. ( 14sqrt{3} ) inches
d. 14 inches
e. ( 7sqrt{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, and the hypotenuse 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 $c$ is the hypotenuse and $a,b$ are the legs of the right - triangle). Here, $x^{2}+7^{2}=14^{2}$. So $x^{2}=14^{2}-7^{2}=(14 + 7)(14 - 7)=21\times7 = 147$.

Step3: Solve for $x$

Take the square root of both sides: $x=\sqrt{147}=\sqrt{49\times3}=7\sqrt{3}$ inches.

Answer:

A. $7\sqrt{3}$ inches