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655-705 (Hard)|   Geometry|      
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nick1816
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Find the area of triangle with sides 13^(1/2), 61^(1/2), and 80^(1/2)? Updated on: 14 May 2019, 06:58
Originally posted by nick1816 on 13 May 2019, 21:22.
Last edited by nick1816 on 14 May 2019, 06:58, edited 3 times in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

54% (01:54) correct 46% (02:30) wrong based on 54 sessions

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Find the area of triangle with sides \(\sqrt{13}\), \(\sqrt{61}\) and \(\sqrt{80}\)?

A. 10
B. 14
C. 20
D. 22
E. 26

Try to think out of box!!!!
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B
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nick1816
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Find the area of triangle with sides 13^(1/2), 61^(1/2), and 80^(1/2)? 14 May 2019, 05:16
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Triangle DEF = Rectangle ABCD - Triangle ABF - Triangle ADE - triangle FCD

Triangle DEF= (8*6)- (0.5*2*3)- (0.5*4*8) - (0.5*6*5)

Triangle DEF= 48-3-16-15=14

Solution by Rohit Ner

nick1816
Find the area of triangle with sides \(\sqrt{14}\), \(\sqrt{61}\) and \(\sqrt{80}\)?

A. 10
B. 14
C. 20
D. 22
E. 26

Try to think out of box!!!!
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behzer0
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Find the area of triangle with sides 13^(1/2), 61^(1/2), and 80^(1/2)? 14 May 2019, 06:51
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in any right triangle with a,b,c sides ==> a^2 + b^2 = c^2

14 + 61 is almost 80 ==> so we can assume that this triangle is almost a right triangle

area of triangle = (1/2) * (14 * 61)^(0.5) = (1/2) * (854)^(0.5) = (almost) (1/2) * (900)^(0.5) = 30/2 = 15

==> B, which is 14, is the closest number to 15
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Find the area of triangle with sides 13^(1/2), 61^(1/2), and 80^(1/2)? 14 May 2019, 07:36
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Lets draw a perpendicular FG on DE and call it y and segment EG as x.

x^2+y^2=13
(sqrt80-x)^2+y^2=61
(sqrt80-x)^2-x^2=61-13=48
80-2sqrt80x=48
16/sqrt80=x=4/sqrt5
y^2=13-16/5=49/5; y=7/sqrt5
Area=1/2*7/sqrt5*4/sqrt5+1/2*(4sqrt5-4/sqrt5)*7/sqrt5
=28/10+1/2*16/sqrt5*7/sqrt5
=2.8+11.2
=14

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Find the area of triangle with sides 13^(1/2), 61^(1/2), and 80^(1/2)? 18 Oct 2023, 02:04
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You can convert the roots in decimal forms, root80=8.9, root61=7.8, root13= 3.6, it would be better if you even forms. Now just put the values in the area of a triangle formula, you will get answers that are very close to 14, so you can just round it up to 14. You might also get answers that are not in the answer options, so you can change the values, You can use this approach, only if you want to get through the sum as quickly as possible, but don't want make any complicated calculations
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