If the length of a rectangle is 3m longer than its width, then: L=W+3 Is the area really 154^2? Or is it 154m^2? If yes, then: A=LW 154=(W+3)(W) 154=(W^2+3W) 0=W^2+3W-154 0=(W-11)(W+14) This means either (W-11) or (W+14) is equal to zero so: W=11 and W=-14 To find out let's substitute the numbers: 154=(11+3)(11) 154=154 Therefore, the width of the rectangle is 11m
By definition the area of a rectangle is given by: A = (w) * (l) Where, w: width l: long We rewrite the expression based on: "The length of a rectangle is 3m longer than its width" A = (w) * (w + 3) We substitute the value of the area: 154 ^ 2 = (w) * (w + 3) Rewrite: 23716 = w ^ 2 + 3w w ^ 2 + 3w-23716 = 0 We solve the polynomial: w = 152.5 Note: the other root is negative. Answer: the width of the rectangle is: w = 152.5 m
