We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
79
1
avatar

\(\text{A shed that measures 8 feet by 11 feet has a brick pathway of constant width built around it, so that the outer edge of the pathway is also a rectangle. The total area of the pathway is 120 square feet. What is its width (in feet)? }\)

 Jul 17, 2019
 #1
avatar+8473 
+2

A shed that measures 8 feet by 11 feet has a brick pathway of constant width built around it, so that the outer edge of the pathway is also a rectangle. The total area of the pathway is 120 square feet. What is its width (in feet)?

The path width is x.

 

\((8+2x)\times (11+2x)-8\times 11=120\\ 88+16x+22x+4x^2-88=120\\ 4x^2+38x-120=0\\ x^2-9,5x-30=0\\ x=4,75\pm\sqrt{4,75^2+30}\\ x=12\)

\(x =-\frac{p}{2}\pm\sqrt{(\frac{p}{2})^2-q}\)

\(x=4,75\pm\sqrt{4,75^2+120}\\ \color{blue} x=12\)

 

The width is 12ft.

laugh  !

 Jul 17, 2019

14 Online Users