What is the relationship between the areas of triangle ABC and triangle DBC in Figure 4?A Equal
b) Area of ABC = 1/2Area of DBC
c)Area of ABC > Area of BDC
d)Area of ABC + 1 = Area of BDC
Answers
You can solve sufficiency questions of geometry by drawing some diagrams too.
Ques3.jpg
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We need to compare areas of ABC and DAB. Notice that given triangle ABC with a particular area, the length of AD is defined. If AD is very small, (shown by the dotted lines) the area of DAB will be very close to 0. If AD is very large, the area will be much larger than the area of ABC. So for only one value of AD, the area of DAB will be equal to the area of ABC.
Now look at the statements:
(1) (AC)^2=2(AD)^2
The area of ABC is decided by AC and BC, not just AC. We can vary the length of BC to see the relation between AC and AD is not enough to say whether the areas will be the same (see diagram). So insufficient.
Ques4.jpg
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(2) ∆ABC is isosceles.
We have no idea about the length of AD so insufficient.
Using both, ratio of sides of ABC are = AC:BC : AB
Area of ABC = 1/2*1*1 = 1/2
Area of DAB =
Areas of both the triangles is the same
Answer:
areas of two triangles are equal
