Can someone check my work, please?
A rectangular pool is twice as long as it is wide. A small walkway surrounds the pool. The walkway is a constant 2 ft wide and has an area of 196 square feet. Find the dimensions of the pool.
What I have:
L=2w+4 and w=w+4
Area of everything= (2w+4)(w+4)
Area of the pool= (2w)w or 2w^2
To find the walkway, I subtract the area of the pool (2w^2) from (2w+4)(w+4).
2w^2+8w+4w+16-2w^2= 12w+16
12w+16= 196 -> w=15
L=2w, w=15 -> 2(15)=30
Width of the pool= 15 ft
Length of the pool= 30 ft
A rectangular pool is twice as long as it is wide. A small walkway surrounds the pool. The walkway is a constant 2 ft wide and has an area of 196 square feet. Find the dimensions of the pool.
What I have:
L=2w+4 and w=w+4
Area of everything= (2w+4)(w+4)
Area of the pool= (2w)w or 2w^2
To find the walkway, I subtract the area of the pool (2w^2) from (2w+4)(w+4).
2w^2+8w+4w+16-2w^2= 12w+16
12w+16= 196 -> w=15
L=2w, w=15 -> 2(15)=30
Width of the pool= 15 ft
Length of the pool= 30 ft