Question

parallelogram PQRS, the length of whose sides are 8 cm and 12 cm, has one diagonal 10 cm long The length of the
other diagonal is approximately​

Answer 1

angle is nessasary to find diagonall...

Answer 2

Given:

• Parallelogram PQRS, the length of whose sides are 8 cm and 12 cm, has one diagonal 10 cm.

To Find:

• Length of other diagonal

Solution:

In parallelogram

we know that,

          $d^2_1+d^2_2=2(l^2+b^2)$

Here,

         $l = 12cm$

         $b = 8cm$

        $d_1 = 10cm$

        $d_2 = ?$

Putting all the values

       ⇒      $10^2 +d^2_2=2(12^2+8^2)$

                $100 +d^2_2=2(144+64)\\\100 +d^2_2=2 \times 208\\d^2_2= 416 - 100\\d_2= \sqrt{316}$

               $d_2 = 2\sqrt{79}cm$

Thus, Other diagonal is $2\sqrt{79} cm$