In the triangle ABC, if AD = 16 and DC = 9 then what is the area of

Question

27th Dec 2019 - Org Post Qn.jpg In the triangle ABC, if AD = 16 and DC = 9 then what is the area of triangle ABC? A.300 B.180 C.175 D.150 E.90

globaldesi · Answer

consider triangle BDC and ABC . Both are similar
thus 
 \frac{9}{BC} = \frac{BC}{25} 
or BC = 15

similarly
consider triangle ADB and ABC . Both are similar
thus 
 \frac{16}{AB}= \frac{AB}{25} 
or AB = 20
area of triangle ABC is given as 
 \frac{1}{2} * AB* BC 
  \frac{1}{2 }* 15*20 
 =150
thus D

vibhu55 · Answer

AD+DC=25.
We now know hypotenuse is 25 so by Pythagorean triplets other sides are 24 and 7.
now area of right angle triangle should be 24*7/2=84. am I wrong?

GMATWhizTeam · Answer

Solution: We are asked the area of riangle ABC = \frac{1}{2} imes BC (base) imes AB (height) . But we have just the value of AD , DC and thus AC . Thie given triangle has 2 right-angle triangles with a common angle \angle C similar.png Thus we can conclude that riangle ABC and riangle BDC are similar by AAA condition of similarity. After proving them similar, we can say that their ratio of corresponding sides will be the same i.e., \frac{AC}{BC} = \frac{BC}{DC} ⇒ BC^2=AC imes DC ⇒ BC^2=25 imes 9 ⇒ BC=\sqrt{25 imes 9} ⇒ BC=5 imes 3=15 Now we have the value of BC . But we still want the value of AB , which we can find very easily using the Pythagoras theorem on riangle ABC . We can say: AC^2=AB^2+BC^2 ⇒ 25^2=AB^2+15^2 ⇒ AB^2=625-225 ⇒ AB^2=400 ⇒ AB=\sqrt{400} ⇒ AB=20 Now area of riangle ABC = \frac{1}{2} imes BC imes AB=\frac{1}{2} imes 15 imes 20 = 150 . Hence the right answer is Option D .

SangamJena · Answer

Concept to know.
A perpendicular drawn to the Hypotenuse divides the traingle to to similar triangles.

Hence in ABD & BDC
AB/DB = DB/DC
DB2 = 16*9.
DB = 4*3 = 12

Now, in triangle ABC.

Height is DB = 12; Base is AC = 25

Area = 1/2 of 12*25 
= 150 , D is our Answer.

Abhishek009 · Answer

Apply Pythagorean tiples form (3 - 4 - 5)...

Here , Hypotenuse is 25 (ie 16 + 9 = 25), thus the other sides will be  15  &  20

So, Area of the Right angled Triangle will be  15*20*\frac{1}{2} = 150 , Answer must be (D)

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In the triangle ABC, if AD = 16 and DC = 9 then what is the area of

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In the triangle ABC, if AD = 16 and DC = 9 then what is the area of

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