Answer:
a = 5
Step-by-step explanation:
Surface Area of a Cuboid
Given a cuboid of dimensions x,y, and z, the surface area is:
A = 2xy + 2yz + 2xz
The first cuboid of dimensions 1,a,9 has a surface area of:
A1 = 2a + 18a + 18 = 20a + 18
The first cuboid of dimensions 2,a,7 has a surface area of:
A2 = 4a + 14a + 28 = 18a + 28
Both areas are equal, thus:
20a + 18 = 18a + 28
Rearranging:
20a - 18a = 28 - 18
2a = 10
a = 5
