ABCD is a parallelogram whose diagonals intersects each other at right angles. If the length of the diagonals are 16 cm and 12 cm then the length of AB
Answers
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.
Answer:
If diagonals intersect each at 90 degrees then They are perpendicular bisectors.
{Name the point O on which they intersect.)
Since diagonal intersect OA = 16/2 = 8cm
OB = 12/2 = 6 cm
Now,
In triangle AOB,
(AB) ^2 = (OA) ^2 + (OB) ^2
(AB) ^2 = (8)^2 + (6)^2
(AB) ^2 = 64 + 36
AB = under root 100
AB = 10 cm
Step-by-step explanation:
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