Two cuboids have the same surface area one is (1 , a , 9) and the other is (2 , a , 7)

what is a?

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