Answer:
Length is 14 in
Width is 8 in
Step-by-step explanation:
<u>Given:</u>
- Length = l
- Width = w
- Perimeter = P = 44 in
<h3>Solution</h3>
<u>Equations as per given:</u>
- l - w = 6
- P= 2(l+w) = 44 ⇒ l +w = 22
<u>Adding up the two equations:</u>
- l - w + l +w = 6 + 22
- 2l = 28
- l = 28/2
- l = 14 in
<u>Then finding the value of w:</u>
- w = l -6
- w = 14 - 6
- w = 8 in
<u>Answer:</u> The length of the rectangle is 14 inches and width is 8 inches
Answer:
a) The coordinates of the missing vertex = (7, 8)
b) Area = 18 square units
Perimeter = 18 units
Step-by-step explanation:
a) We know three of the four vertices:
A: (4, 2) C ______ D(?)
B: (7, 2) | |
C: (4, 8) A |______| B
To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:
Hence, the distance of point D from point C in the x-direction is:
Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:
Then, the distance of point D from point B in the y-direction is:

Therefore, the coordinates of the missing vertex (point D) are:
b) The area of the rectangle is:

The perimeter is given by:

I hope it helps you!
Supposing the sides with 6 and 8 is a right angle, you can create a new line from C and P, and find the length using the equation of a²+b²=c² or 6²+8²=c², with c equaling the radius of the circle.
After finding c, you will have to find the length from C to the midpoint of AC, using the same equation a²+b²=c². If both the lengths of C to the midpoint of AC, and A to the midpoint of AC are equal, you can do b+b to find the length of AC.
Using the same approach, you can find AB. Hope this makes sense, if not, I can clarify more.