Question

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.

Answer 1

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

$L=3W+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Since the area of a rectangle is the product of its length and width, so we must have

$A=L\times W\\\\\Rightarrow 95=(3W+4)W\\\\\Rightarrow 3W^2+4W-95=0\\\\\Rightarrow 3W^2+19W-15W-95=0\\\\\Rightarrow W(3W+19)-5(3W+19)=0\\\\\Rightarrow (W-5)(3W+19)=0\\\\\Rightarrow W-5=0,~~~~~3W+19=0\\\\\Rightarrow W=5,~-\dfrac{19}{3}.$

Since the width of the rectangle cannot be negative, so we get

$W=5~\textup{cm}.$

From equation (i), we get

$L=3\times5+4=15+4=19~\textup{cm}.$

Thus, the length and width of the rectangle are 19 cm and 5 cm respectively.