Chapter Review
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Use the formula for the area of a rectangle A=l w. Write an equation that can be solved for l, which you can solve by completing the square.
28 centimeters
To find the perimeter of the credit card we need to know its width and its length. Let's determine these values using the given information. Recall the formula for the area of a rectangle. A=l w Here l is the length of the rectangle and w is the width of the rectangle. In our case A= 46.75. We also know that the width w is 3 centimeters shorter than the length l, so w= l-3. We will substitute these values into the formula. By doing so we obtain an equation that can be solved for l.
A= 46.75, w= l-3
Rearrange equation
Distribute l
Let's solve this equation by completing the square. We will follow five steps.
Let's get started! We will identify the value of b first. l ^2-3l=46.75 ⇔ l ^2+( - 3)l=46.75 Therefore, b= - 3. Next we will find one half of b. - 3/2=- 1.5 Moving on to Step 2, we have to square our result. (- 1.5)^2=1.5^2=2.25 Let's add 2.25 to both sides of the equation.
Now we are able to write the left-hand side of the equation as the square of a binomial. l ^2-3l+2.25=49 ⇔ (l-1.5)^2=49 Finally, we will take a square root of both sides of the equation. Remember to calculate the positive and negative square roots.
sqrt(LHS)=sqrt(RHS)
Calculate root
LHS+1.5=RHS+1.5
The solutions to the equation are 1.5+7=8.5 and 1.5-7=- 5.5. Since l represents the length of the card, it cannot be negative. Therefore, l= 8.5 centimeters and w= 8.5-3=5.5 centimeters. Now we can calculate the perimeter of the card. We will use the formula for the perimeter of a rectangle. P=2l+2w Let's substitute l=8.5 and w=5.5!
The perimeter of the credit card is 28 centimeters.