Question
If the area of a rhombus-shaped box is 6√7cm2 and its one diagonal is 6cm. Find the side of the rhombus.
Answer: Option C
:
C
Let the side of the rhombus = a
Area of the triangle containing the diagonal = 12 times area of the rhombus
One of the diagonal = 6 cm
Semi perimeter = 6+a+a2=a+3
Now the area of the triangle containing the diagonal =√s(s−a)(s−b)(s−c)
3√7 = √(a+3)(a+3−a)(a+3−a)(a+3−6)
=√(a+3)(a−3)(9)
= √(a2−9)(9)
We take square on both sides and get,
63 = (a2−9)×9
⇒(a2−9) = 7
⇒a2 = 7+9 = 16
⇒a= 4cm
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:
C
Let the side of the rhombus = a
Area of the triangle containing the diagonal = 12 times area of the rhombus
One of the diagonal = 6 cm
Semi perimeter = 6+a+a2=a+3
Now the area of the triangle containing the diagonal =√s(s−a)(s−b)(s−c)
3√7 = √(a+3)(a+3−a)(a+3−a)(a+3−6)
=√(a+3)(a−3)(9)
= √(a2−9)(9)
We take square on both sides and get,
63 = (a2−9)×9
⇒(a2−9) = 7
⇒a2 = 7+9 = 16
⇒a= 4cm
Was this answer helpful ?
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