The length of a rectangle is 3 centimeters less than four times its width. Its area is 10 square centimeters. Find the dimensions of the rectangle.

Answer:W = 2 cmL = 5 cmStep-by-step explanation:A rectangle is a four sided shape with 4 perpendicular angles. It has two pairs of parallel sides which are equal in distance: width and length. Its area, the amount of space inside it, can be found using the formula A = l*w. If the area is 10 cm² and the length is "3 cm less than 4 times the width" or 4w - 3, you can substitute and solve for w. A = l*w10 = (4w - 3)(w)10 = 4w² - 3wSubtract 10 from both sides to make the equation equal to 0. Then solve the quadratic by quadratic formula.4w² - 3w - 10 = 0Substitute a = 4, b = -3 and c = -10.[tex]w = \frac{3 +/- \sqrt{(-3)^2 - 4(4)(-10)} }{2(4)} = \frac{3 +/- \sqrt{9 +160)} }{8} =  \frac{3 +/- \sqrt{169} }{8} = \frac{3+/-13}{8}[/tex]There are two possible solutions which can be found.3 + 13 / 8 = 16/ 8 = 23 - 13 / 8 = -10/8 = -5/4Since w is a side length or distance, it must be positive so w = 2 cm.If the width is 2 cm then the length is 4(2) - 3 = 8 - 3 = 5 cm.