Question

PYRAMIDS The Great Pyramid in Giza, Egypt has a square base with side lengths of 5x yards and a height of 4x –

Answer 1

Answer:

The value of x is equal to $50\ yd$

The side length of the base b is $250\ yd$

The height h is $150\ yd$

Step-by-step explanation:

we know that

The volume of a square Pyramid is equal to

$V=\frac{1}{3} b^{2}h$

where

b is the length side of the square base

h is height of the pyramid

In this problem we have

$V=3,125,000\ yd^{3}$

$b=5x\ yd$

$h=4x-50\ yd$

substitute and solve for x

$3,125,000=\frac{1}{3} (5x)^{2})(4x-50)$

$9,375,000=100x^{3} -1,250x^{2}\\ \\100x^{3} -1,250x^{2}-9,375,000=0$

using a calculator

The value of x is equal to

$x=50\ yd$

Find the dimensions of the pyramid

The side length of the base b

$b=5(50)=250\ yd$

The height h

$h=4(50)-50=150\ yd$