Math, asked by sreeroop497, 7 months ago

ABCD is a parallelogram whose diagonals intersects each other at right angles. If the length of the diagonals are 16cm and 12cm , then the perimeter of the parallelogram is _________ *

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Answered by Anonymous

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

=>
$\sqrt{25}$
= 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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Answered by angelatom35

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.

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