Answer:
The value of x is equal to [tex]50\ yd[/tex]
The side length of the base b is [tex]250\ yd[/tex]
The height h is [tex]150\ yd[/tex]
Step-by-step explanation:
we know that
The volume of a square Pyramid is equal to
[tex]V=\frac{1}{3} b^{2}h[/tex]
where
b is the length side of the square base
h is height of the pyramid
In this problem we have
[tex]V=3,125,000\ yd^{3}[/tex]
[tex]b=5x\ yd[/tex]
[tex]h=4x-50\ yd[/tex]
substitute and solve for x
[tex]3,125,000=\frac{1}{3} (5x)^{2})(4x-50)[/tex]
[tex]9,375,000=100x^{3} -1,250x^{2}\\ \\100x^{3} -1,250x^{2}-9,375,000=0[/tex]
using a calculator
The value of x is equal to
[tex]x=50\ yd[/tex]
Find the dimensions of the pyramid
The side length of the base b
[tex]b=5(50)=250\ yd[/tex]
The height h
[tex]h=4(50)-50=150\ yd[/tex]
