1) the measure of opposite side of a parallelogram are 7x + 20 cm and 8x - 30 cm find the length of the sides. 2) one of the diagonal of a rhombus is equals to one of its sides find the angles of the Rhombus
Answers
Question 1) :- the measure of opposite side of a parallelogram are 7x + 20 cm and 8x - 30 cm find the length of the sides ?
Solution :-
we know that , Opposite sides of a parallelogram are equal to each other.
So,
→ 7x + 20 = 8x - 30
→ 8x - 7x = 20 + 30
→ x = 50cm.
Therefore,
→ Length of 2 given sides will be = 7x + 20 = 7*50 + 20 = 350 + 20 = 370 cm. (Ans.)
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Question 2) :- one of the diagonal of a rhombus is equals to one of its sides find the angles of the Rhombus ?
Solution :-
we know that, all the sides of a rhombus are equal in length .
So,
we can conclude that, when diagonal of a rhombus is equal to one of its sides , than it will be equal to all sides.
Than,
Triangle made my 2 adjacent sides of rhombus and diagonal have all sides are equal. Therefore, it a Equaliteral Triangle.
- Each angle of an Equaliteral Triangle is equal to 60° .
Therefore,
→ Angle between to adjacent sides of rhombus also = 60° .
Now, we also know that, Opposite angles of a rhombus have equal .
Hence, Opposite angle is also equal to 60°.
Let rest to angles are x° each.
Than,
→ x + x + 60° + 60° = 360° . (Angle sum Property).
→ 2x + 120° = 360°
→ 2x = 360° - 120°
→ 2x = 240°
→ x = 120° .
∴ all angles of given rhombus are (60°, 120°, 60°, 120°.)