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# The length of one of the sides of a triangle is 25 units. If the area

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Senior DS Moderator
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The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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Updated on: 04 Nov 2018, 07:33
2
00:00

Difficulty:

65% (hard)

Question Stats:

27% (02:35) correct 73% (01:41) wrong based on 26 sessions

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The length of one of the sides of a triangle is 25 units. If the area of the triangle is 120 units^2 and the length of the another side of the triangle is 10 units. Find the length of the third side.
A) $$\sqrt{255}$$
B) $$\sqrt{585}$$
C) $$\sqrt{572}$$
D) $$\sqrt{558}$$
E) 24

Weekly Quant Quiz #7 Question No 7

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Originally posted by gmatbusters on 03 Nov 2018, 09:14.
Last edited by gmatbusters on 04 Nov 2018, 07:33, edited 1 time in total.
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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03 Nov 2018, 09:59
USing pythagoras theorem ans E
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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03 Nov 2018, 10:05
The length of one of the sides of a triangle is 25 units. If the area of the triangle is 120 units^2 and the length of the another side of the triangle is 10 units. Find the length of the third side.

so lets say a = 25, b =10 and area = 120

so 3rd side cannot be greater than 35 (sum of 2 sides) and also should be at least greater than 15 as (>15+10 ) will be greater than side being 25

area of triangle = 1/2 * side * perpendicular

E cannot be the solution as we know 1/2*24*10 becomes 120 but it has to be right angled triangle which does not satisfies Pythagorus theorem. (AB^2+BC^2= AC^2)

area calculation possibility = 1/2 * side *25 or 1/2*side *10

option A: sqrt (255) close to 16 as 16 square is 256 hence 1/2*16*25= 120
option B: sqrt (585) is greater than 24 and hence none of the area calculation possibility fits here
Option C: sqqrt(572) is less than 24 and hence none of the area calculation possibility fits here
option D: sqrt (558) is less than 24 and hence does not fit any of the area calculation possibility

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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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03 Nov 2018, 11:19
2
Given -

base*height = 240, other side = 25

Let Base = 10, Height = 24.

Now, we have $$24^2 +7^2 = 25^2$$
So, the perpendicular will be at distance of 7 from side with length 25.

Length of other side = $$24^2 + 3^2$$ = 585
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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03 Nov 2018, 12:00
root585
Herons Formula s=(35+c)/2
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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04 Nov 2018, 01:37
Area of ABC = 1/2 * 25 * AD = 120

BD^2 = 100 - 92.16 = 7.84
BD = 2.8

DC = 22.2

AC = 22.2^2 + 9.6^2
=√585
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Re: The length of one of the sides of a triangle is 25 units. If the area &nbs [#permalink] 04 Nov 2018, 01:37
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