State whether the statement is true or false.
A right triangle ABC is right-angled at A. Also, BCED, ACFG, and ABMN are squares on the sides BC, CA, and AB respectively such that AX ⊥ DE and cuts BC at Y. Then ar (BCED) = ar (ABMN) + ar (ACFG).

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True

False

answer is A.

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Detailed Solution

Given that, right triangle ABC is right-angled at A. Also, BCED, ACFG, and ABMN are squares on the sides BC, CA, and AB respectively such that AX ⊥ DE and cuts BC at Y.
The following figure depicts the given situation.
Question Image

ABC is a right angle triangle at A, we can apply the Pythagoras theorem.

B C 2 = A B 2 + A C 2

. [1]
The area of the square BCDE =

B C 2

. [2]
The area of the square ACFG =

A C 2

. [3]
The area of the square ABMN =

A B 2

. [4]
Using equations [2] [3] and [4] in [1] we get:

a r (B C E D) = a r (A B M N) + a r (A C F G)

.
Hence, the statement is true and the correct option is 1.

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