Knowledge and procedure: EASY 10 POINTS!!?

Question

A rectangular swimming pool measures 50 by 25 metres. A path around the edge of the pool is "x" metres wide on each side.

a) Calculate the area of the pool

b) Determine an expression for the length of the pool plus the path.

c) Determine an expression for the width of the pool plus the path.

d) Determine an expression for the area of the pool plus the path

e) Expand this expression

f) Find an expression for the area of the path

g) If the path is 2.3 metres wide, calculate the area of the path

Answer 1

Pool       Length = 50m       Breadth = 25m

Path       Width  = x m

a)  Area of pool = length * breadth = 50*25 = 1250 m^2

b)  Length of (pool +path) = 50+2x

c)  Width of (pool + path) = 25+x+x  =   25 +2x

d)  Area of (pool+path) = length*width = (50+2x)(25+2x)

e)  Area  = 4x^2 + 150x + 1250

f)   Area of path = Area of (path +pool) - Area of pool

    = (4x^2 +150x+1250) -1250   = 4x^2 + 150x

g)  x = 2.3 m  Area of path = 4x^2 +150x

     Area of path = 4(2.3)^2 + 150(2.3)  =  366.16 m^2

CHEERS !!!

Answer 2

a)

Area = 50 * 25 m²

Area = 1250m²

b)

Length = 50 + 2x

c)

Width = 25 + 2x

d)

Area = (50 + 2x)(25 + 2x)

e)

Area = 1250 + 100x + 50x + 4x²

Area = 4x² + 150x + 1250

f)

Area = (4x² + 150x + 1250) - 1250

Area = 4x² + 150x

g)

Area = 4x² + 150x

Area = 4*2.3² + 150(2.3)

Area = 21.16 + 345

Area = 366.6 m²