Write an equation that could help determine the width, w, of the walkway.

Question

a rectangle garden measures 13 meters by 17 meters and has a cement walkway around the perimeter. the width of the walkway remains constant on all 4 sides. the garden walkway has a combined area of 396 sq. meters. Write an equation that could help determine the width, w, of the walkway.

Answer 1

if you draw a picture you see that the walkway has sides of length 13 + 2w and 17 + 2w where w is the width.

 

the area of the corners is w² and there are 4 corners so that is 4w²

 

The other 4 pieces have areas of 13w (2 of these) and 17w (2 of these)

 

Putting it all together we have 2(13w) + 2(17w) + 4w² = 396 m²

 

26w + 34w + 4w² = 396

 

4w² + 60w - 396 = 0       divide by 4

 

w² + 15w - 99 = 0          this is the equation to determine width of the walkway