Question

Share

In a room a bulb is fixed at a point $O$ on the ceiling. Just below the bulb a large table is placed as shown in Fig. 7.40. A cardboard is cut in the form of quadrilateral $A B C D$ and is fixed between the bulb and the table. When bulb is switched on, shadow $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ of cardboard $A B C D$ is formed on the top of the table such that quadrilateral $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is an enlargement of quadrilateral $A B C D$ with scale factor $1: 2$. If $A B=1.5 cm, B C=2.5 cm, C D=2.4 cm, A D=2.1 cm$, $\angle A=105^{\circ}, \angle B=100^{\circ}, \angle C=70^{\circ}$ and $\angle D=85^{\circ} cm$, answer the following questions:

(i) The measurement of $\angle A^{\prime}$ is
(a) $105^{\circ}$ $\qquad$ (b) $100^{\circ}$ $\qquad$ (c) $70^{\circ}$ $\qquad$ (d) $80^{\circ}$
(ii) The sum of the angles $\angle A^{\prime}$ and $\angle C^{\prime}$ of quadrilateral $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is(a) $185^{\circ}$ $\qquad$ (b) $205^{\circ}$ $\qquad$ (c) $175^{\circ}$ $\qquad$ (d) $155^{\circ}$
(iii) Perimeter of quadrilateral $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is
(a) 8.5 cm $\qquad$ (b) 5 cm $\qquad$ (c) 10 cm $\qquad$ (d) 17 cm
(iv) The length of side $A^{\prime} B^{\prime}$ of quadrilateral $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is
(a) 1.5 cm $\qquad$ (b) 3 cm $\qquad$ (c) 2.5 cm $\qquad$ (d) 5 cm