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555-605 (Medium)|   Geometry|      
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Bunuel
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The length of one of the sides of a triangle is 13 units. If the area 28 Dec 2022, 10:30
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Difficulty:

55% (hard)

Question Stats:

44% (02:45) correct 56% (02:43) wrong based on 9 sessions

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The length of one of the sides of a triangle is 13 units. If the area of the triangle is 90 units^2 and the length of the another side of the triangle is 15 units. Find the length of the third side.

(A) √124
(B) √134
(C) √224
(D) √234
(E) √244
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E
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The length of one of the sides of a triangle is 13 units. If the area 28 Dec 2022, 15:08
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Bunuel
The length of one of the sides of a triangle is 13 units. If the area of the triangle is 90 units^2 and the length of the another side of the triangle is 15 units. Find the length of the third side.

(A) √124
(B) √134
(C) √224
(D) √234
(E) √244
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Given, two sides of a triangle are 13 and 15 units, and area of the triangle is 90 units square

To find -> measurement of the third side

Let's say, we make a triangle ABC with sides AB = 15 units and BC = 13 units. Let's draw a perpendicular CD from C to AB
The area of the triangle = 1/2 * AB * CD
Or, 90 = 1/2 * 15 * CD
>> CD = 12 units

Now, using the pythagoras theorem in triangle CDB-
CB^2 = CD^2 + DB^2
13^2 = 12^2 + DB^2
169 = 144 + DB^2
169 - 144 = DB^2
25 = DB^2
Or, DB = 5 units

AD = AB - DB
AD = 15 - 5
AD = 10 units

Now, applying pythagoras theorem in triangle CDA-
AC^2 = CD^2 + AD^2
AC^2 = 12^2 + 10^2
AC^2 = 144 + 100
AC^2 = 244
Or, AC = √244

Hence, (E) is the correct answer
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