Answer:
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
