MODEL QUESTION PAPER FOR PRACTICE
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Q. 5. Solve any one of the following subquestions :
(i) Area of a rhombus is 50/3 sq. units. One of
its diagonal is 10 units, then
(a) Find the length of its other diagonal.
(b) Using the diagonal property of rhombus and the
concept of Pythagoras theorem find the length of side
of rhombus.
(c) Find the perimeter of rhombus.
Answers
Step-by-step explanation:
i) a) Area of rhombus = 1/2 × product of its diagonals
Let the other diagonal be x
50/3 = 1/2 × 10 × x = 5 × x
15x = 50
x = 50/15 = 10/3
The other diagonal is 10/3 units .
b) In a rhombus the diagonals bisect each other at right angles .
Consider a rhombus ABCD and AC and BD as its diagonals and O is the point where the diagonals bisect each other.
< AOD = 90⁰
BD= 10 units and OD = 5 units
AC = 10/ 3 units and OA = 5/3 units
Consider triangle AOD and <AOD = 90⁰
By using phythagorans theorem
AO² + OD² = AD²
(5/3)² + (5²) = AD²
AD² = 25/9 + 25 = 25 + 225 /9 = 250/9
AD = root 250/9 = 5 root 10 / 9
The length of side of rhombus is 5 root 10 / 9 units
c) Perimeter of rhombus = 4 × side
= 4 × 5 root 10/9
= 20 root 10 / 9 units
The perimeter of rhombus = 20 root 10 / 9 units
HOPE this helps you. Please mark it as the branlisist
Thank you