Alex drew a shape that belongs to both the category of rhombuses and the category of rectangles.
1 answer:
You might be interested in
X=29 and y=10
You would isolate one of the variables and then plug the expression into the other equation to find the value of one variable. Then you would plug this value into the other equation to determine the value of the remaining variable.
You would isolate one of the variables and then plug the expression into the other equation to find the value of one variable. Then you would plug this value into the other equation to determine the value of the remaining variable.
Answer:
Total area equation = tex]w(w+6)=91[/tex]
b/2 = 3
Dimensions of the patio: width = 7 feet, length = 13 feet
Step-by-step explanation:
The area of a rectangle is given the formula:
where
is the width
is the length
We know from our problem that the area of the patio is 91 square feet, so . We also know that the length is 6 feet longer then the width, so
.
Replacing values in our area equation
Expanding the left side:
Remember that to complete the square we need to add half the coefficient of the linear term squared. The lineal term is , so its coefficient is 6. Now, half its coefficient or
. Finally,
.
To complete the square we need to add 9 to both sides of the equation:
Notice that the left side is a perfect square trinomial (both and 9 are perfect squares), so we can express it as:
Now that we completed the square, we can solve our equation
- Take square root to both sides
- Subtract 3 from both results
Since length cannot be negative, is the solution of our equation.
We now know that the width of our rectangular patio is 7 feet, so we can find its length:
We can conclude that half the coefficient of the width is , the width of the patio is 7 feet, and its length is 13 feet.