As with all Geometry questions, let’s start with what’s given and correlate it to the given figure. In triangle ABC, the following things are given:
AC = 9 cm
CB = 25 cm
CD = 15 cm
Angle CDB = 90 degrees.
Therefore, triangle CDB is a right angled triangle.
Now, consider the ratio of the length of sides,
CD and CB. CD : CB = 15 : 25 = 3 : 5.
Now, recall that for a Pythagorean triangle, all sides are in the ratio 3 : 4 : 5
Applying that principle to triangle DCB, let CD = 3x, CB = 5x and BD = 4x.
Now, we know that, CB = 25
Therefore, x = 25/5 = 5.
Now, therefore, BD = 4x = 4 x 5 = 20.
Again using the Pythagorean principle, we can say that
AC = 3y, CD = 5y and AD = 4y.
Now, we know that AC = 3y = 9.
Therefore, y = 9/3 = 3. So, AD = 4y = 4 x 3 = 12.
Therefore, AB = AD + DB = 12 + 20 = 32 cm.
Now, to calculate area of triangle ABC, we know that
Area = ½ x b x h = ½ x AB x CD
Therefore, Area = ½ x 32 x 15 = 16 x 15 = 240 cm2
If you had chosen Option A, then you might have calculated only the area of triangle CDB.
If you had chosen Option D, then you might have calculated only the area of triangle ACD.
If you had chosen Option B, then it is possible that you may have miscalculated the length of AB as 22 cm.
Keep an eye out for those booby traps!
Good Luck! Try the 91Èȱ¬ Style Questions next! :)
