Answer
Length $= 168$ ft
Width $= 42$ ft
Work Step by Step
$x =$ width
$4x =$ length
1. Find $x$
Let $P =$ perimeter of the rectangle
$2(4x) + 2(x) = 420$
$8x + 2x = 420$
$10x = 420$
$x = 42$
2. Substitute $x$ into the length and width equations
a) Width
$x = 42$ ft
Therefore the width of the rectangular building is $= 42$ ft
b) Length
$4x = 4(42)$
$4x = 168$ ft
Therefore the length of the rectangular building is $= 168$ ft.
