MATH SOLVE

2 months ago

Q:
# The area of a rectangular fountain is (x^2 + 12x +20) feet squared. The width is (x + 2) feet.I solved Part A (Find the length of the fountain) which is (x + 10) and Part B (A 2-foot walkway is built around the fountain. Find the dimensions of the outside border of the walkway) which are x + 4 feet by x + 12 feet, but I'm having trouble finding the answer for Part C.Part C: Find the total area covered by the fountain and walkway.

Accepted Solution

A:

Part A:

The total area = x² + 12x + 20 = (x+2)(x+10)

The width = x+2

∴ Length = area / width = [ (x+2)(x+10) ] / (x+2) = x+10

Part B:

A 2-foot walkway is built around the fountain

∴ The width = (x+2) + 2 + 2 = x + 6

The length = (x+10) + 2 + 2 = x +14

Part C:

the total area covered by the fountain and walkway.

= (x+6)(x+14)

= x² + 20 x + 84

See the attache figure for more explanation

The total area = x² + 12x + 20 = (x+2)(x+10)

The width = x+2

∴ Length = area / width = [ (x+2)(x+10) ] / (x+2) = x+10

Part B:

A 2-foot walkway is built around the fountain

∴ The width = (x+2) + 2 + 2 = x + 6

The length = (x+10) + 2 + 2 = x +14

Part C:

the total area covered by the fountain and walkway.

= (x+6)(x+14)

= x² + 20 x + 84

See the attache figure for more explanation