A rectangle has a length of 34 inches less than 5 times it’s width. If the area of the rectangle is 867 square inches, find the length of the rectangle.

Length of the rectangle is 51 inchesSolution:Given that Length of the rectangle in 34 miles less than 5 times its width Area of rectangle = 867 square inches Need to determine length of the rectangle. Let assume width of the rectangle be represented by variable x. So 5 times width of the rectangle =5x 34 inches less than 5 times width of the rectangle = 5x – 34 As Length of the rectangle in 34 miles less than 5 times its width => Length of the rectangle = 5x – 34 The formula for rectangle is given as:[tex]\text { area of rectangle }=length \times width[/tex]As given that Area of rectangle = 867 square inches[tex]\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}[/tex]On solving quadratic equation by using quadratic formula[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]In our case a = 5, b = -34 and c = -867On substituting value of a, b and c in quadratic formula we get[tex]\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}[/tex]Since x represents width, it cannot be negative, so x = 17Length of the rectangle = 5x – 34 = 5(17) – 34 = 51 Hence length of the rectangle is 51 inches