|
|
GMAT 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.
01 Nov 2021, 06:45
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
33% (02:23) correct
67%
(02:51)
wrong
based on 21
sessions
History
Date
Time
Result
Not Attempted Yet
In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336, what is the perimeter of the triangle?
A. 58
B. 77
C. 82
D. 84
E. 92
A. 58
B. 77
C. 82
D. 84
E. 92
01 Nov 2021, 07:56
Kudos
Bookmarks
Attaching solution to the above problemo.
Attachments
Solution - 1.jpg [ 2.52 MiB | Viewed 1279 times ]
01 Nov 2021, 11:19
Kudos
Bookmarks
Draw a triangle ABC
Use side AC = 28 as the Base
Drop an altitude from vertex B to base AC ——> call the point D where this height is perpendicular to side AC
Let BD = h
(1/2) (28) (h) = 336
350 is divisible by 7 ———-> 50th positive multiple of 7
Thus 350 - 14 = 336 ——-> 336 is the 48th positive multiple of 7
336/7 = 48
(1/2) (4) (h) = 48
h = 24
We know have right triangle BDA:
Leg BD = 24
Leg AD = ?
Hypotenuse AB = 30
This is a multiple of the Pythagorean triplet 3-4-5
(6) (4) = 24
(6) (5) = 30
Thus AD must be = (6) (3) = 18
DC = (side AC) - (AD)
DC = (28) - (18) = 10
We now have right triangle BDC
Let BD = 24
Leg DC = 10
Hypotenuse BC = ?
This is a multiple of the Pythagorean Triplet 5-12-13
(2) (5) = 10
(2) (12) = 24
Thus, side BC = hypotenuse must be = (2) (13) = 26
We now have our unknown side to complete the perimeter.
BC = 26
Perimeter = 26 + 28 + 30 ——-> or (3) (28) = 60 + 24 =
84 answer
(Tried to include some of the speed math tricks to make the calculation move more quickly)
Posted from my mobile device
Use side AC = 28 as the Base
Drop an altitude from vertex B to base AC ——> call the point D where this height is perpendicular to side AC
Let BD = h
(1/2) (28) (h) = 336
350 is divisible by 7 ———-> 50th positive multiple of 7
Thus 350 - 14 = 336 ——-> 336 is the 48th positive multiple of 7
336/7 = 48
(1/2) (4) (h) = 48
h = 24
We know have right triangle BDA:
Leg BD = 24
Leg AD = ?
Hypotenuse AB = 30
This is a multiple of the Pythagorean triplet 3-4-5
(6) (4) = 24
(6) (5) = 30
Thus AD must be = (6) (3) = 18
DC = (side AC) - (AD)
DC = (28) - (18) = 10
We now have right triangle BDC
Let BD = 24
Leg DC = 10
Hypotenuse BC = ?
This is a multiple of the Pythagorean Triplet 5-12-13
(2) (5) = 10
(2) (12) = 24
Thus, side BC = hypotenuse must be = (2) (13) = 26
We now have our unknown side to complete the perimeter.
BC = 26
Perimeter = 26 + 28 + 30 ——-> or (3) (28) = 60 + 24 =
84 answer
(Tried to include some of the speed math tricks to make the calculation move more quickly)
Posted from my mobile device
