If the sum of the lengths of the diagonals of a rhombus is 10 m and if its area is 9 m2. then, what is the sum of squares of the diagonals?
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Answered by
7
Let ABCD is the rhombus where AC and BD are the diagonals.
Area of rhombus=1/2×AC×BD
9=1/2×AC×BD
18=AC×BD
AC+BD=10
(AC+BD)=10
(AC+BD)^2=10^2
AC^2+BD^2+AC.BD=100
AC^2+BD^2+2×18=100
AC^2+BD^2+36=100
AC^2+BD^2=64
Area of rhombus=1/2×AC×BD
9=1/2×AC×BD
18=AC×BD
AC+BD=10
(AC+BD)=10
(AC+BD)^2=10^2
AC^2+BD^2+AC.BD=100
AC^2+BD^2+2×18=100
AC^2+BD^2+36=100
AC^2+BD^2=64
Answered by
3
Answer:
Step-by-step explanation:
Let ABCD be a rhombus whose diagonals are AC and BD, we are given that the sum of the lengths of the diagonals of a rhombus is 10 m and its area is 9 m2, therefore
⇒
Also,
Now, squaring both sides of the above equation, we get
Therefore, the sum of the squares of the diagonals is 64.
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