GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
What is the length of hypotenuse K?
[#permalink]
Updated on: 12 Apr 2019, 11:25
Updated on: 12 Apr 2019, 11:25
5
Bookmarks
00:00
Question Stats:
62% (02:55) correct
37% (02:31) wrong based on 32 sessions
Hide Show timer Statistics
Attachment:
#GREpracticequestion What is the length of hypotenuse K.jpg [ 27.04 KiB | Viewed 8358 times ]
What is the length of hypotenuse K?
Show: :: OA
7.8
Re: Find the length of hypotenuse K
[#permalink]
12 Apr 2019, 21:07
12 Apr 2019, 21:07
4
1
Bookmarks
LT2018 wrote:
Any more explanations for this question?
Plz see the diag. below
As
Now the left hand triangle is a 5-12-13 triangle (Pythagorean triplet) ( it can also be derived by Pythagoras theorem as the unknown side = \(\sqrt{13^2 - 12^2} = 5\)
Since the left part of the triangle has got the base 5, hence the base of the other triangle = 12.2 - 5 = 7.2
Now both triangles are similar ( Angle - angle -angle)
and hence the side can be deduced in the form:
\(\frac{7.2}{12}= \frac{k}{13}\)
or \(k = 7.8\)
Attachments
#GREpracticequestion What is the length of hypotenuse K.jpg [ 30.78 KiB | Viewed 8214 times ]
Re: What is the length of hypotenuse K?
[#permalink]
11 Jun 2021, 22:39
11 Jun 2021, 22:39
1
1
Bookmarks
Begin by noting that the triangle on the left is a 5–12–13 Pythagorean
triple, so the bottom side is 5. Subtract 12.2 – 5 = 7.2 to get the bottom side of
the triangle on the right.
Next, the two unmarked angles that “touch” at the middle must sum to 90°,
because they form a straight line together with the right angle of 90° between
them, and all three angles must sum to 180°. Mark the angle on the left x. The
angle on the right must then be 90 – x.
Now the other angles that are still unmarked can be labeled in terms of x.
Using the rule that the angles in a triangle sum to 180°, the angle between 12
and 13 must be 90 – x, while the last angle on the right must be x,
Since each triangle has angles of 90, x, and 90 – x, the triangles are similar.
This observation is the key to the problem. Now you can make a proportion,
carefully tracking which side corresponds to which. The 7.2 corresponds to
12, since each side is across from angle x. Likewise, k corresponds to 13,
since each side is the hypotenuse. Write the equation and solve for k:
7.2/12=k/13
k=13*7.2/12
k=7.8
triple, so the bottom side is 5. Subtract 12.2 – 5 = 7.2 to get the bottom side of
the triangle on the right.
Next, the two unmarked angles that “touch” at the middle must sum to 90°,
because they form a straight line together with the right angle of 90° between
them, and all three angles must sum to 180°. Mark the angle on the left x. The
angle on the right must then be 90 – x.
Now the other angles that are still unmarked can be labeled in terms of x.
Using the rule that the angles in a triangle sum to 180°, the angle between 12
and 13 must be 90 – x, while the last angle on the right must be x,
Since each triangle has angles of 90, x, and 90 – x, the triangles are similar.
This observation is the key to the problem. Now you can make a proportion,
carefully tracking which side corresponds to which. The 7.2 corresponds to
12, since each side is across from angle x. Likewise, k corresponds to 13,
since each side is the hypotenuse. Write the equation and solve for k:
7.2/12=k/13
k=13*7.2/12
k=7.8
