A rectangular pond 5 meters by 7 meters is going to be built.

Question

A rectangular pond 5 meters by 7 meters is going to be built. The builders want the pond to be surrounded by a walkway x meters wide. Write an equation that represents the area of the pond with the walkway included

Length: y=x+5 Width: y=x+7

 

 

Using your equation, what is the area of the region when: 

 

x=1  x=2  x=3  

Answer 1

It doesn't really matter which you label

as length or width.  The area of the pond

is L*W = 35m²

 

Since you are putting a rectangular border

of width x meters around the pond... each

dimension, length and width are expanded by 2x..

not x.  Thus, Norbert is correct that your problem

is incorrectly stated.  The new dimensions are

Length: 2x+5, Width: 2x + 7

 

The area of the pond and walkway together is:

(2x+5)(2x+7) 

= 2x(2x) + 2x(7) + 5(2x) + 5(7)

= 4x² + 24x + 35

 

For x =1:  4(1²) + 24(1) + 35 = 63 m²

 

For x =2:  4(2²) + 24(2) + 35 = 16+48+35 = 99 m²

 

For x = 3:  4(3²) + 24(3) + 35 = 36+72+35 = 143 m²