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Question

Construct a ΔABC in such a way that ABC=45, CAB=45 and AB = 7 cm. Construct a rectangle, the area of which is equal to the area of ΔABC. What are the dimensions of the rectangle?


  1. (4, 9)

  2. (3.5, 3.5)

  3. (7, 8)

  4. (4, 5)


Solution

The correct option is B

(3.5, 3.5)


Method of Construction:

(1) Draw a line segment AT and then the part AB = 7 cm is cut from AT.
(2) Draw BAX=45 at A of AT. Draw YBA=45 at B of AT. Let AX and BY intersect at C. Then, ABC is the required triangle.
(3) Draw PQ through C parallel to AB.
(5) Draw perpendicular bisector MN of AB, which intersects PQ at E.
(6) Cut EF from EQ, equal to DB.
(7) Join F and B.

EFDB is the required rectangle (in this case all sides are the same)
Its dimensions are (3.5,3.5)

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