Question

The height of an equilateral rectangular prism decreases by two units. The new lateral area is less than the original by how much?

two times the area of the base

two less than the perimeter of the base

two less than the the area of the base

two times the perimeter of the base

Answer 1

two less than the the area of the base

Answer 2

^what i think

Answer 3

@jim_thompson5910

Answer 4

The lateral area is

LSA = 2*(LH+WH)

if the height decreases by 2, then H becomes H-2, meaning that we get

LSA = 2*(L(H-2)+W(H-2))

LSA = 2*(LH-2L+WH-2W)

LSA = 2*(LH+WH-2L-2W)

LSA = 2*(LH+WH)+2*(-2L-2W)

LSA = 2*(LH+WH)-2*(2L+2W)


Notice how the first piece 2*(LH+WH) is the original lateral surface area. Also, notice how the new lateral surface area is the result of subtracting off double the perimeter


So it's really "two times the perimeter of the base"

Answer 5

So decreasing the height by 2 means that the new lateral surface area is less by 2 times the perimeter of the base.