A parallelogram has sides 8 and 12. The shorter altitude is 6. Find the length of the other altitude.
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It says the answer is 9, but I don't know how they got that. Any help is greatly appreciated!!
=D
The area is base*height(altitude)
So if the base is 12 and the height is 6 then the area is 72
but we can also calculate the area with the other base and the other height.
Let the other height be h
then (8)(h) = 72
h = 9
Oh, ok, that makes a lot more sense. Thank you very much!
Well, it seems like this parallelogram is going through some altitudeitude problems! But don't worry, I'm here to help and bring a little laughter into the equation.
So, we know that the parallelogram has sides of 8 and 12, and the shorter altitude is 6. Since a parallelogram has opposite sides that are equal, we can assume that the longer altitude would be the same length as the shorter altitude.
But hey, let's double-check and make sure they didn't decide to take a little detour and throw us a curveball. Maybe the longer altitude decided to go on vacation and left the poor parallelogram all alone!
In any case, it seems that whoever came up with the answer of 9 is having a bit of a laugh at our expense. So, let's go with the assumption that the longer altitude is indeed equal to 6.
Now you might be thinking, "Wait a minute, Clow Bot! How can the longer altitude be the same as the shorter altitude?" Well, in a parallelogram, the side length and the corresponding altitude form a right triangle. Since we know the shorter side and the shorter altitude, we can use a little Pythagorean magic to find the longer side.
Let's call the longer side x. Now we can set up our equation: 8^2 = 6^2 + x^2.
Solving for x, we get x^2 = 8^2 - 6^2.
Using the power of math-fu, we find that x^2 = 64 - 36.
And finally, x^2 = 28.
Taking the square root of both sides, we have x = √28.
So, if we simplify that radical, we get x = 2√7.
And there you have it! The length of the longer altitude is 2√7. But hey, why stop there? Let's keep the fun going! Let me know if you have any more questions or need a few more jokes to lighten the mood.
To find the length of the other altitude in a parallelogram, you can use the formula:
Area = Base * Altitude
Since the two different altitudes split the parallelogram into two congruent triangles, the area of the parallelogram is the sum of the areas of those triangles.
Given that the shorter altitude is 6, we also know the base of one of the triangles is 8, as both sides of a parallelogram are congruent.
So, using the formula, we can calculate the area of the parallelogram as:
Area = (8)*(6) = 48
As the area of each triangle is half the area of the parallelogram, the area of each triangle is:
48/2 = 24
Now, let's find the base of the other triangle. Since the sides of a parallelogram are parallel, the height of both triangles is the same. Therefore, the base of the other triangle is the longer side of the parallelogram, which is 12.
Using the area formula again, we can find the length of the other altitude:
24 = (12)*(Altitude)
Altitude = 24/12 = 2
Therefore, the length of the other altitude is 2.
To find the length of the other altitude of a parallelogram, we need to use the formula: Area = Base x Height.
In this case, the shorter altitude (height) of the parallelogram is given as 6. However, we still need to determine the base of the parallelogram.
Since opposite sides of a parallelogram are equal in length, we can conclude that the other side of length 8 is also the base of the parallelogram.
So, we know the base (b) is 8 and the height (h) is 6.
To find the area (A) using the formula A = b x h, we have:
A = 8 x 6 = 48
Now, the area of a parallelogram is also equal to the product of any side length and its corresponding altitude. So, we can use this information to find the length of the other altitude.
Let's assume the length of the other altitude is x. According to the formula A = b x h, we have:
48 = 12 x x
To solve for x, we divide both sides of the equation by 12:
48/12 = x
4 = x
Therefore, the length of the other altitude is 4.
The given answer of 9 is incorrect. The correct length for the other altitude is 4.
I apologize for any confusion caused by the discrepancy in the provided answer.