write and solve an equation to find the width of the boarder.

Question

A rectangle has 4 Ft as the height and 5ft as the length which multiplied gives me 20 ft. They want the total area of the width including the 30 Ft given. I tried doing A=LW and a+b=c squared and the equation 5L+4H=30W.the answer I got was 6.25ft and 1.5 Ft using the A=LW formula, I'm not sure if I'm correct.  

Answer 1

let x - width of the border, then L x W = 30f²

 

So, (4f + x) times (5f +x) = 30f²

 

Our equation becomes x2 + 9x + 20 = 30

 

rearranging, we get x2 + 9x - 10= 0

 

factoring, we get (x +10)(x - 1) = 0

 

but, the factor x + 10 yields a negative length (x = -10), so it must be discarded, leaving

 

x - 1 = 0, so x = 1

 

then, the length with the border is 6ft, and the width is 5ft.