Sure, let's solve for [tex]\( a \)[/tex] step by step starting from the given formula for the volume of a right square pyramid:
[tex]\[ V = \frac{1}{3} a^2 h \][/tex]
1. Multiply both sides by 3 to clear the fraction:
[tex]\[ 3V = a^2 h \][/tex]
2. Divide both sides by [tex]\( h \)[/tex] to isolate [tex]\( a^2 \)[/tex]:
[tex]\[ a^2 = \frac{3V}{h} \][/tex]
3. Take the square root of both sides to solve for [tex]\( a \)[/tex]:
[tex]\[ a = \sqrt{\frac{3V}{h}} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{a = \sqrt{\frac{3V}{h}}} \][/tex]
Looking at the options given:
A. [tex]\( a = 3 \sqrt{\frac{h}{V}} \)[/tex]
B. [tex]\( a = \sqrt{\frac{3}{V}} \)[/tex]
C. [tex]\( a = \sqrt{\frac{37}{h}} \)[/tex]
D. [tex]\( a = \sqrt{\frac{3V}{h}} \)[/tex]
The correct answer is option D: [tex]\( a = \sqrt{\frac{3V}{h}} \)[/tex].
