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ABCD is a rectangle. Let E be a point on AB and F a point on CD such that DE is parallel to BF.If AE = 3 cm and if the area of \( \Large \triangle BFC \) = 6 sq cm.
Consider the following statements.
Area of rectangle ABCD can be of the form \( \Large pq^{2} \) sq cm, where p, q are distinct primes.
Area of the figure EBFD is of the form \( \Large r^{2} \)sq cm, where r is rational but 5 not an integer.
Which of the above statements is/are correct?

A) Only I
B) Only II
C) Both l and II
D) Neither I nor II

Correct Answer:

A) Only I

Description for Correct answer:

Given that,

Area of \( \Large \triangle BFC \) = \( \Large 6 cm^{2} \)

\( \Large \frac{1}{2} \times 3 \times x\times \) =6 =>x=4cm

In \( \Large \triangle BFC, BF^{2}=4^{2}+3^{2}=16+9 \)

=> \( \Large BF^{2}=25 \)

=> BF=5

Area of rectangle ABCD \( \Large pq^{2} \)=\( \Large p(2)^{2} cm^{2} \)

Which is of the form \( \Large pq^{2} \).

While the area of EBFD cannot be the form of \( \Large r^{2} cm^{2} \)

Part of solved Area and perimeter questions and answers : >> Elementary Mathematics >> Area and perimeter

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