Find the area and perimeter of a rectangle with a base of 8in and a height of 5 in.
(1 point)
Responses
P = 54 in and A = 54 in^2
P = 44 in and A = 40 in^2
P = 40 in and A = 26 in^2
P = 26 in and A = 40 in^2
I apologize for the confusion caused by the missing image in the question. I tried my best to provide accurate responses based on the information given. I'm glad to hear that most of the information provided was correct, and I appreciate your understanding. If you have any more questions or need further assistance, please let me know.
To find the perimeter of a rectangle, you add all the sides together. The formula for the perimeter of a rectangle is P = 2(l + w), where l is the length and w is the width.
In this case, the base of the rectangle is given as 8 inches and the height is given as 5 inches. Therefore, the length (l) is 8 inches and the width (w) is 5 inches.
Plugging those values into the formula, we get P = 2(8 + 5) = 2(13) = 26 inches.
So the perimeter of the rectangle is 26 inches.
To find the area of a rectangle, you multiply the length and width. The formula for the area of a rectangle is A = l * w.
Plugging in the values from the given problem, we get A = 8 * 5 = 40 square inches.
So the area of the rectangle is 40 square inches.
Therefore, the correct response is:
P = 26 in and A = 40 in^2.
If the perimeter of a square is 24 in, what is the area?(1 point)
Responses
A = 22 in^2
A = 36 in^2
A = 576 in^2
A = 96 in^2
To find the area of a square, you need to know the length of one side. However, in this case, only the perimeter of the square is given, which is 24 inches.
The formula for the perimeter of a square is P = 4s, where s represents the length of one side.
Since the perimeter is given as 24 inches, we can set up the equation 24 = 4s.
Dividing both sides of the equation by 4, we find that s = 6 inches.
Now that we know the length of one side, we can find the area of the square using the formula for area, A = s^2.
Plugging in the value of s as 6 inches, we get A = 6^2 = 36 square inches.
So the area of the square is 36 square inches.
Therefore, the correct response is:
A = 36 in^2.
HK¯¯¯¯¯¯¯¯¯
bisects ∠GKJ. ∡HKJ = 5x+4
and ∡HKG = 9x−4
. Solve for x and the m<GKJ
(1 point)
Responses
x = 2 m<GKJ = 28 degrees
x = 2 m
x = 5 m<GKJ = 14 degrees
x = 5 m
x = 2 m<GKJ = 32 degrees
x = 2 m
x = 5 m<GKJ = 32 degrees
To solve for x and the measure of <GKJ, we can use the fact that the angles of a triangle add up to 180 degrees.
From the given information, we know that ∠HKJ = 5x+4 and ∠HKG = 9x-4, and that HK¯¯¯¯¯¯¯¯¯ bisects ∠GKJ.
Since HK¯¯¯¯¯¯¯¯¯ bisects ∠GKJ, it means that ∠HKJ and ∠HKG are equal to each other.
So we can set up an equation: 5x+4 = 9x-4.
We can then solve this equation for x by isolating the variable:
5x+4 = 9x-4
4+4 = 9x-5x (subtract 5x from both sides to isolate x)
8 = 4x
8/4 = x
x = 2
Now that we have found the value of x, we can substitute it back into one of the angle measurements to find the measure of <GKJ. Let's use ∠HKJ = 5x+4.
m<GKJ = 5(2)+4
m<GKJ = 10+4
m<GKJ = 14 degrees
So the correct response is:
x = 2 m<GKJ = 14 degrees
HK¯¯¯¯¯¯¯¯¯
bisects ∠GKJ. ∡HKJ = 5x+4
and ∡HKG = 9x−4
. Solve for x and the m<GKJ
(1 point)
Responses
x = 2 m<GKJ = 28 degrees
x = 5 m<GKJ = 14 degrees
x = 2 m<GKJ = 32 degrees
x = 5 m<GKJ = 32 degrees
Apologies for the confusion in the previous response. Let's go through the problem again.
Given that HK¯¯¯¯¯¯¯¯¯ bisects ∠GKJ and the measures of ∡HKJ and ∡HKG are 5x+4 and 9x-4 respectively, we can set up an equation with the angles:
∡HKJ = ∡HKG
5x+4 = 9x-4
To solve for x, we need to isolate the variable on one side of the equation:
4x = 8
Dividing both sides of the equation by 4:
x = 2
Now that we have found the value of x, we can substitute it back into one of the angle measurements to find the measure of ∡GKJ. Let's use ∡HKJ = 5x+4:
∡HKJ = 5(2)+4
∡HKJ = 10+4
∡HKJ = 14 degrees
So the correct response is:
x = 2 m<GKJ = 14 degrees
your answer was wrong but okay
I apologize if my previous response was incorrect. I will reevaluate the problem and provide the correct solution.
Given that HK¯¯¯¯¯¯¯¯¯ bisects ∠GKJ and the measures of ∡HKJ and ∡HKG are 5x+4 and 9x-4 respectively, we can set up an equation with the angles:
∡HKJ = ∡HKG
5x + 4 = 9x - 4
To solve for x, we'll isolate the variable on one side of the equation:
4 + 4 = 9x - 5x
8 = 4x
Dividing both sides of the equation by 4:
2 = x
Now that we have found the value of x, we can substitute it back into one of the angle measurements to find the measure of ∡GKJ. Let's use ∡HKJ = 5x + 4:
∡HKJ = 5(2) + 4
∡HKJ = 10 + 4
∡HKJ = 14 degrees
So the correct response is:
x = 2 ∡GKJ = 14 degrees