Suppose that the length of a certain rectangle is four centimeters more than three times its width. If the area of the rectangle is 95 square centimeters, find its length and width.
Accepted Solution
A:
Answer: The length and width of the rectangle are 19 cm and 5 cm respectively.Step-by-step explanation: Given hat the length of a rectangle is four centimeters more than three times its width and the area of the rectangle is 95 square centimeters.We are to find the length and width of the rectangle.Let W and L denote the width and the length respectively of the given rectangle.Then, according to the given information, we have[tex]L=3W+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]Since the area of a rectangle is the product of its length and width, so we must have[tex]A=L\times W\\\\\Rightarrow 95=(3W+4)W\\\\\Rightarrow 3W^2+4W-95=0\\\\\Rightarrow 3W^2+19W-15W-95=0\\\\\Rightarrow W(3W+19)-5(3W+19)=0\\\\\Rightarrow (W-5)(3W+19)=0\\\\\Rightarrow W-5=0,~~~~~3W+19=0\\\\\Rightarrow W=5,~-\dfrac{19}{3}.[/tex]Since the width of the rectangle cannot be negative, so we get[tex]W=5~\textup{cm}.[/tex]From equation (i), we get[tex]L=3\times5+4=15+4=19~\textup{cm}.[/tex]Thus, the length and width of the rectangle are 19 cm and 5 cm respectively.