Question

a rectangular garden is 3ft longer than it is wide. its area is 460 ft squared. what are its dimensions​

Answer 1

Answer:

$\large \boxed{\text{23 ft by 20 ft}}$

Step-by-step explanation:

        Let x = the width of the garden

Then x + 3 = the length of the garden

Area of garden = length × width

                      A = lw = x(x+ 3)

$\begin{array}{rcl}x( x+ 3)& = & 460\\x^{2} + 3x& = &460\\x^{2} + 3x - 460& = &0\\x + 23 = 0 & \text{or} & x - 20 = 0\\x = -23 & \text{or} & \mathbf{x = 20}\\\end{array}$

 width = x                    = 20 ft

length = x + 3 = 20 +3 = 23 ft

$\text{The dimensions of the garden are \large \boxed{\textbf{23 ft by 20 ft}} }$

Check:

$\begin{array}{rcl}20(20 + 3) & = &460\\20(23) & = & 460\\460 & = & 460\\\end{array}$

OK.