x: width
z: length
The length of a rectangle is 17 inches longer than the width (x) means:
z = x + 17
The area of a rectangle is computed as follows:
Area = x*z
Replacing with Area = 1334 and z = x+17:
1334 = x*(x + 17)
Applying distributive property:
1334 = x*x + x*17
0 = x² + 17x - 1334
Using the quadratic formula:
[tex]\begin{gathered} x_{1,2}=\frac{-17\pm\sqrt[]{17^2-4\cdot1\cdot(-1334)}}{2\cdot1} \\ x_{1,2}=\frac{-17\pm\sqrt[]{5625}}{2} \\ x_1=\frac{-17+75}{2}=29_{} \\ x_2=\frac{-17-75}{2}=-46_{} \end{gathered}[/tex]
Given that x cannot be negative, then the answer is x = 29 inches
