The area of a rectangle is 66 ft2, and the length of the rectangle is 1 ft more than twice the width. Find the dimensions of the rectangle.
Answers
The length and width of the rectangle is 12 feet and 5.5 feet respectively given that the area of a rectangle is 66 feet², and the length of the rectangle is 1 feet more than twice the width. This can be obtained by finding algebraic expression for length by assuming width to be b and solving the quadratic equation formed after substituting it in the formula of area of rectangle.
What is the formula of area of a rectangle?
Area of a rectangle,
A= l × b, where A is the area, l is the length and b is the width.
Find algebraic expression for length:
Let us assume that width of the rectangle is b.
Given that, length of the rectangle is 1 feet more than twice the width
⇒ l = 2b+1 is the required expression.
Calculate the length and width:
Given that A= 66 feet²
In the formula, A= l × b we can substitute the expression for length.
66=(2b+1)b
2b²+b=66
⇒ 2b²+b-66=0
The quadratic equation can be solved using splitting the middle term,
2b²+12b-11b-66=0
2b(b+6)-11(b+6)=0
(2b-11)(b+6)=0
b=11/2 or b= - 6
Taking positive value of b, b=11/2⇒b=5.5 feet
Substitute for length, l = 2b+1 = 2(11/2)+1=11+1 =12 ⇒l = 12 feet
Hence the length and width of the rectangle is 12 feet and 5.5 feet respectively given that the area of a rectangle is 66 feet², and the length of the rectangle is 1 feet more than twice the width.
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w = n
l = 2n+1
w*l = 66
n(2n+1) = 66
2n^2 + n =66
2n^2 + n - 66 = 0
using quadratic equation
n = 11/2
width = 11/2 = 5.5
length = 11 + 1 = 12
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Answers
Answer:
6cm is the missing length
Step-by-step explanation:
See the 10cm and the 4cm?
If you look at in a way if you added 6 more centimeters to the 4cm it would be 10, leaving 6cm as the missing length.
Answers
Answer: The answer is -1/8 :)
B.)Add 6 to both sides
C.) Divide both sides by 5
D.) Multiply both sides by 2
Answers
9514 1404 393
Answer:
B.) Add 6 to both sides
Step-by-step explanation:
Actually, the first step is to look at the given equation and at what is being asked. The next step is to formulate a strategy for finding what is asked.
Here, the equation is ...
As part of our assessment of this, we notice that ...
- x is multiplied by 2/5
- 6 is subtracted
We are asked for the first step to solve this equation. The usual strategy for solving such an equation is to undo the steps done to the variable, in reverse order. In the above assessment, we notice the last step is subtracting 6 from the product. So, our first step in finding the value of x is to undo that subtraction:
add 6 to both sides
__
Additional comment
We also notice as part of our assessment that the equation contains the fraction 2/5, which has a denominator of 5. If we choose to eliminate fractions as a first step in our solution strategy, we would multiply both sides by 5. Notice that this is not one of the offered choices.
Answer:
A) Add One-sixth to both sides.
Step-by-step explanation:
Answers
Answer:
1.225km is equal to each laps
Step-by-step explanation:
Since Kristy total distance traveled = 29.6km
And Kristy ran 24 laps and later walk 0.2km. it simply implies that
Total distance traveled = distance covered running + distance covered walking
Since we know that
Total distance traveled = 29.6km
distance covered running = 24 laps
distance covered walking = 0.2km
Distance covered running in km = total distance traveled - distance covered walking
Distance covered running in km = 29.6km - 0.2km = 29.4km.
To now find the distance for each lap.
Since we have:
Distance covered running in km = 29.4km.
Distance covered running in lap = 24 laps
i.e
24 laps = 29.4km
1 lap = x
Use cross-multiple
24 laps * x = 29.4km × 1 lap
x = 29.4km / 24
x = 1.225km
Therefore
1.225km is equal to each laps.
totaldistanceof24laps
29.6km - 0.2km
=29.4km
totaldistanceofeachlap
24 laps = 29.4km
1 lap = ?
Usecross-multiple
24 laps × X = 29.4km × 1 lap
X = 29.4km / 24
X = 1.225km
Answer
1.225km