Question

The area of a rectangular book shelf is 28 square feet.The length is 2 feet longer than the width.What are the dimensions of the book shelf to the nearest tenth? DRAW DIAGRAM.

Answer 1

ANSWER

Dimensions: W = 4.39 ft; L = 6.39 ft

(a) See explanation

(b) 0 = W² + 2W - 28

(c) W = 4.39 ft

EXPLANATION

(a)

(b) We know that the length is 2 feet longer than the width of the shelf,

$L=W+2$

And the area, which is the product of the width and the length is 28ft²,

$28=L\cdot W$

Replace the first equation into the second,

$28=(W+2)W$

This is a quadratic equation. We can rewrite it in standard form,

$28=W^2+2W$$0=W^2+2W-28$

(c) To solve this equation we can use the quadratic formula,

$\begin{gathered} 0=ax^2+bx+c \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}$

In our equation, a = 1, b = 2 and c = -28,

$W=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-28)}}{2\cdot1}$$W=\frac{-2\pm\sqrt[]{4+112}}{2}$$W=\frac{-2\pm\sqrt[]{116}}{2}\approx\frac{-2\pm10.77}{2}$

One of the results is negative, so we will discard it - a width cannot be negative. We have to use the result with the sum,

$W=\frac{-2+10.77}{2}=4.39$

The width of the shelf is 4.39 feet, rounded to the nearest hundredth.

Then, we just have to replace W into the first equation to find the length of the shelf,

$L=W+2=4.39+2=6.39ft$