State true or false:

In the figure given below, the ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of triangle ACD.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Here, we have to find whether the ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of triangle ACD or not.
Question Image

The area of any triangle with given base and altitude measurements is half the sum of its base and altitude.
Now, in the given figure, the altitude AD is common for the triangles

Δ A B C

and

Δ A C D

, while their bases are BC and CD respectively.
So, the ratio of their areas can be given as follows,

area (Δ ABC) area(Δ ACD) = 12 × BC × AC 12 × CD × AC = BC CD

So, the ratio of the areas of

Δ A B C

and

Δ A C D

is obtained as BC: CD.
Therefore, we conclude that the ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of triangle ACD.
Hence, the statement is true.
Hence, the correct option is (1).

Watch 3-min video & get full concept clarity