(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.
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