Question

Construct a $\Delta ABC$ in such a way that $\angle ABC={45}^{\circ }$, $\angle CAB={45}^{\circ }$ and AB = 7 cm. Construct a rectangle, the area of which is equal to the area of $\Delta ABC$. What are the dimensions of the rectangle?

• A. (3.5, 3.5)
• B. (7, 8)
• C. (4, 5)
• D. (4, 9)

Answer 1

The correct option is A

(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 $\angle BAX={45}^{\circ }$ at A of AT. Draw $\angle YBA={45}^{\circ }$ 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.

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