ABCD is a parallelogram whose digonals intersect each other at right angles . if the length of the diagonal is 6 cm and 8 cm , find the length ?
Answers
Answer:
ABCD is a parallelogram whose diagonals intersect each other at O with 90°.
so it's a rhombus as diagonals of rhombus interest each other at right angles.
diagonal1 (AC) = 6cm
diagonal 2(BD) = 8cm
OD = OB = 3cm each
OA = OC = 4cm each
Let, us take triangle AOB
it is a right angled triangle
=> (OA)² + (OB)² = (AB)²
=> (4)² + (3)² = (AB)²
=> 16 + 9 = (AB)²
=> 25 = (AB)²
=> = AB
=> 5 = AB
So, AB = 5cm
AB = BC = CD = AD (all sides of rhombus are equal)
Each side of the parallelogram ABCD is 5cm.
Step-by-step explanation:
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Answer:
your answer :
Lenght of diagonals
BD = 6 CM
AC= 8 CM
intersect each other at right angles
i.e ✓AOB = ✓BOC = ✓COD = ✓DOA = 90 °
By the property of a parallelogram
Draganals bisect each other.
i-e OA = OC & OB = OD
or OA = OC 1/2 AC & OB = OD = 1/2 BD
=) OA = OC = 1/2 × 8 & OB = OD = 1/2 × 6
OA = OC = 4 & OB = OD = 3
taking right ∆AOB, Using Pythagoras Theorem
(AB)² = 6A ² +(0B)²
(AB)² = 4² +3²
(AB)² = 16+9
(AB)² = 25
(AB)² = (5)²
=) AB=5
Similarly we can find BC, CD & AD
by taking ∆es ( angles ) Boc, COD & DOA
i-e same as AB.
Sides of the parallelogram
AB = BC = CD = DA = 5 cm
Step-by-step explanation:
i hope it helps you :)