# Solving problems with Quadratic Equation

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## Presentation Transcript

### Hello this video will teach how to solve problems with quadratic equation :

Hello this video will teach how to solve problems with quadratic equation

### A rectangular lot has an area of 96m2. What are the dimensions of the lot if it requires 40m of fencing materials to enclose it? :

A rectangular lot has an area of 96m 2. What are the dimensions of the lot if it requires 40m of fencing materials to enclose it?

### First we should know what is the formula for a rectangular lot which is l * w = a and the formula for the perimeter of a rectangle which is 2l+2w=p :

First we should know what is the formula for a rectangular lot which is l * w = a and the formula for the perimeter of a rectangle which is 2l+2w=p Using these formulas, we can form a quadratic equation that can get the dimensions of the lot.

### Next is we should substitute the given to these formulas and we would get: :

Next is we should substitute the given to these formulas and we would get: l * w= 96 2l + 2w= 40

### Now we are going to focus first on the formula on how to get the area of a rectangle :

Now we are going to focus first on the formula on how to get the area of a rectangle

### :

Remove one of the two variables on the equations by multiplying both sides with either w or l and the result is : l= 96/w or w= 96/w depending on which variable are you removing. We will be using l=96/w but you can also use the other one because it will still give the same answer.

### Next we will substitute what you result is to the formula on how to get the perimeter of a rectangle :

Next we will substitute what you result is to the formula on how to get the perimeter of a rectangle This is how it should look like: 2(96/w) + 2w) = 40

### Next step is to make it into a quadratic equation It should be like this : 2w2-40w+192 :

Next step is to make it into a quadratic equation It should be like this : 2w 2 -40w+192

### We will be solving for the roots by using quadratic formula but you can use any method you want. :

We will be solving for the roots by using quadratic formula but you can use any method you want.

### First find a, b, and c Then let x be the width :

First find a, b, and c Then let x be the width

### Then substitute these to the quadratic formula, it would look like these: :

Then substitute these to the quadratic formula, it would look like these:

### :

Continue solving it..

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Continue solving it..

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Then solve for X 1 and X 2 …..

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

### X1=12 X2=8 :

X 1 =12 X 2 =8 Now we would just divide x1 and x2 to the area to get the length

### The lengths are: :

The lengths are: l 1 =8 l 2 =12

### Therefore the dimensions are 12x8 m :

Therefore the dimensions are 12x8 m 