Question

I don't get it can someone help me.

Answer 1

EXPLANATION

Let's see the facts:

Length = 12+ 2*Width =12+2w

Width=w

Area= 14cm^2

The area of the rectangle is given by the following relationship:

$\text{Area}_{\text{rectangle}}=Length\cdot Width$

Replacing terms:

$14=(12+2\cdot\text{Width)}\cdot\text{Width}$

To make it more simple, let's call w to the width and apply the distributive property:

$14=12w+2w^2$

Subtracting -14 to both sides:

$0=2w^2+12w-14$

Applying the quadratic roots formula:

$w_1,w_2=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}$

We have a=2, b=12 and c=-14

Replacing terms:

$w_1,w_2=\frac{12\pm\sqrt[]{12^2-4\cdot2\cdot(-14)}}{2\cdot2}$

Multiplying numbers:

$w_1,w_2=\frac{12\pm\sqrt[]{144-112}}{4}$

Subtracting numbers:

$w_1,w_2=\frac{12\pm\sqrt[]{32}}{4}=\frac{12\pm4\sqrt[]{2}}{2}=6\pm2\sqrt[]{2}$

The solutions to the quadratic equation are:

$w_1=8.82,w_2=3.17$

We have two possible solutions, w_1=8.82 cm and w_2=3.17 cm. Let's take w_2=3.17 cm as a solution:

The length would be as follows:

$\text{length}=12+2\cdot3.17=18.34\operatorname{cm}$

The answers are:

Width = 3.17 cm = 317/100 cm

Length = 18.34 cm = 917/50 cm