Question

nsc sept mathematics p2|2026
question 7
below is a triangular pyramid box a candy store uses on special requests for themed birthday parties. it consists of four triangles. line ab = √3x, cb = x, acd = α, and adb = 60°. ab is perpendicular to cb and bd.
7.1 determine the length of ac in terms of x.

Explanation:

Step1: Identify right - triangle

In right - triangle ABC, angle ABC = 90°, AB = $\sqrt{3}x$ and CB = x.

Step2: Apply Pythagorean theorem

The Pythagorean theorem states that in a right - triangle $a^{2}+b^{2}=c^{2}$, where c is the hypotenuse and a, b are the other two sides. Here, $AC^{2}=AB^{2}+CB^{2}$. Substitute AB = $\sqrt{3}x$ and CB = x into the formula: $AC^{2}=(\sqrt{3}x)^{2}+x^{2}=3x^{2}+x^{2}=4x^{2}$.

Step3: Solve for AC

Take the square root of both sides of the equation $AC^{2}=4x^{2}$. Since AC represents a length and must be non - negative, $AC = 2x$.

Answer:

$AC = 2x$