Question 1126554
area of a rectangle is length * width.


let L = length and let W = width.


area of a rectangle becomes L * W.


if the length is 23 feet more than the width, then L = W + 23.


replace L with W + 23 in the formula and you get area of a rectangle = (W + 23) * W.


simplify to get area of the rectangle = 23W + W^2


since the area is 6840, then the formula becomes 6840 = 23W + W^2


subtract 6840 from both sides of the equation and re-order the terms in descending order of degree and flip sides to get:


W^2 + 23W - 6840 = 0


factor this quadratic equation to get:


(W+95) * (W-72) = 0


solve for W to get W = -95 or W = 72.


W can't be negative, so W = 72.


since L = W + 23, then L = 95


length is 95 and width is 72


area is length * width = 95 * 72 = 6840.


length is 23 greater than width.


solution looks good.


solution is length = 95 and width = 72.


even though the quadratic was factor-able, if it wasn't obvious what the factors needed to be, then use the quadratic formula to find the answer.