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.
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Step-by-step explanation:
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
=>
\sqrt{25}
25
= AB
=> 5 = AB
So, AB = 5cm
AB = BC = CD = AD (all sides of rhombus are equal)
Each side of the parallelogram ABCD is 5cm.