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The perimeter of isosceles ΔABC is 32, and the length of one
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21 May 2019, 01:28
21 May 2019, 01:28
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The perimeter of isosceles \(ΔABC\) is 32, and the length of one side is 10. The height, measured from the vertex where the two equal sides meet, is 8.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The length of the longest side of ΔABC |
12 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: The perimeter of isosceles ΔABC is 32, and the length of one
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24 May 2019, 08:00
24 May 2019, 08:00
1
For isosceles triangle according to the question the perimeter is 2x + y = 32.
The question says one of the side is 10. So the triangle could be a 10,10,12 or it could be 11,11, and 10.
Now, the question also says that the perpendicular dropped from the vertex of the point joining two equal sides is 8.
so picture a figure such as the one below:
grepic.JPG [ 91.02 KiB | Viewed 4601 times ]
Now there are two right triangles inside the triangle ABC. Each of these triangle follow pythagoras theorem. If x = 10 then the length of segment y = 12. If on the other hand x =11 then by pythagoras theorem the length of y = 2* \(\sqrt{57}\) which is not equal to 10. Therefore ABC should have a length of 10,10,12 and therefore the longest side is 12.
The question says one of the side is 10. So the triangle could be a 10,10,12 or it could be 11,11, and 10.
Now, the question also says that the perpendicular dropped from the vertex of the point joining two equal sides is 8.
so picture a figure such as the one below:
Attachment:
grepic.JPG [ 91.02 KiB | Viewed 4601 times ]
Now there are two right triangles inside the triangle ABC. Each of these triangle follow pythagoras theorem. If x = 10 then the length of segment y = 12. If on the other hand x =11 then by pythagoras theorem the length of y = 2* \(\sqrt{57}\) which is not equal to 10. Therefore ABC should have a length of 10,10,12 and therefore the longest side is 12.
Re: The perimeter of isosceles ΔABC is 32, and the length of one
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28 May 2019, 11:49
28 May 2019, 11:49
1
Carcass wrote:
The perimeter of isosceles \(ΔABC\) is 32, and the length of one side is 10. The height, measured from the vertex where the two equal sides meet, is 8.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The length of the longest side of ΔABC |
12 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Use the approach of Check for EQUALITY...
so, lets say longest side = 12, then sides are 12,10,10.
Now, height from vertex (where similar sides meet i.e. 10 & 10) = 8 and it will cut the side 12 into half (isosceles triangle)
so, we have a triplet of right angle triangle - 10,6, 8 (given in question)
So, our assumption was correct. Hence, C
