Question

The pyramid shown below has a square base, a height of 7, and a volume of 84. what is the length of the side of the base?

Answer 1

Volume of a pyramid is (length * width * height) / 3

So we plug in the given information and solve. Let x = length and width since it's a square their measurements are the same.

84 = (x * x * 7) or 84 = 7x²

Divide both sides by 7 to isolate the squared variable. 

x² = 12

Now square root both sides to isolate the variable

x = √12 which simplifies to x = 2√3

The measurements for the length and width of the base are 2√3 units or approximately 3.464 units. 

Answer 2

The length of the side of the base is 6 units.

What is the volume of the pyramid?

The volume of the pyramid is;

$\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base$

The pyramid shown below has a square base, a height of 7, and a volume of 84.

Substitute all the values in the formula

$\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base\\\\\rm84 =\dfrac{1}{3}\times height \times 7\\\\Height = \dfrac{84\times 3}{7}\\\\ Height = \dfrac{252}{7}\\\\Height =36$

The length of the side of the base is;

$\rm Side\ length^2=height\\\\ Side\ length^2=36\\\\Side\ length^2=6^2\\\\Side\ length=6$

Hence, the length of the side of the base is 6 units.

Learn more about pyramid here;

https://brainly.com/question/17615619

#SPJ2