question_answer

(a) Construct a quadrilateral BLUE in which BL = 5.3 cm, BE = 2.9 cm,                                                                 \[\angle B=70{}^\circ ,\]                                                                  \[\angle L=95{}^\circ\]  and                                                                 \[\angle U=85{}^\circ .\]

(b) A student attempted to draw a quadrilateral PLAY, where PL = 3 cm, LA = 4 cm, AY = 4.5 cm, PY = 2 cm, LY = 6 cm, but could not draw it. What is the reason?

Answer:

(a) (i) Draw BL = 5.3 cm.

(ii) Draw                                                                \[\angle B=70{}^\circ\] with the help of rough figure..

(iii) Making                                                        \[\angle BLU=\text{ }95{}^\circ\] with the help of rough figure, since

\[\angle B+\angle L+\angle U+\angle E=\text{ }360{}^\circ\]

or                             \[70{}^\circ +95{}^\circ +85{}^\circ +\angle E=360{}^\circ\]

or                                       \[250{}^\circ \text{ }+\angle E=\text{ }360{}^\circ\]

or                                   \[\angle E=\text{ }360{}^\circ \text{ }\text{ }250{}^\circ\]

\[\angle E=\text{ }110{}^\circ\]

(iv) Making \[\angle BEY=\text{ }110{}^\circ \] intersecting EY and LZ at U.

(v) Join EU and LU, then BLUE is a required quadrilateral.

(b) No, we can?t draw it, because                                                     \[PL+\text{ }PY\text{ }<\text{ }LY.\] actually the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.