To create a giant gemstone, Sara first made two identical square pyramids that each had a base area of 100 square inches. Then
she glued the pyramids’ bases together to form the gemstone.
The surface area of the gemstone is 520 square inches. What is the
value of x?

The value of x is 21 inches

Step-by-step explanation:

We are given that  Sara first made two identical square pyramids that each had a base area of 100 square inches.

Area of square base =Side^2

So,

Side = Side^2=100

Side = 10

So, Side of square base = 10 inches

We are given that she glued the pyramids’ bases together to form the gemstone. The surface area of the gemstone is 520 square inches.

So, Surface area of two identical square pyramids  = 520 sq.in.

Surface area of one square pyramid  = 520/2=260sq.in

Formula of area of square pyramid = A=2bs+b^2

Where s is the height of each triangular surface and b is the side of square base

b = 10

We are given that the height of each triangular surface is x

So, s=x

So,  area of 1 square pyramid = 2(10)x+(10)^2

So, 2(10)x+(10)^2=520

20x+100=520

20x=420

x=21

Hence the value of x is 21 inches

x/3-10=8

x/3=18

x=48