Question

Abcd is a parallelogram with ab = 21 cm, bc = 13 cm and bd= 14 cm. What is the length of ac.

Answer 1

Answer:

the length of ac is 12cm

Answer 2

The length of AC=32 cm

Step-by-step explanation:

In parallelogram ABCD

AB=21 cm

BC=13 cm

BD=14 cm

We know that

Sum of square of diagonals=2(Sum of square of sides of parallelogram)

AC and BD are diagonals of parallelogram .

By using the formula

$AC^2+BD^2=2(AB^2+BC^2)$

Substitute the values

$AC^2+(14)^2=2((21)^2+(13)^2)$

$AC^2+196=2(441+169)$

$AC^2+196=1220$

$AC^2=1220-196=1024$

$AC=\sqrt{1024}$

AC=32 cm

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