Question

The perimeter of a rectangle is
- 22p3 + 32p2q2+ 16pq and one of its sides is - 6p3 + 7p²q2 + pq. Find its other side. ​

Answer 1

Answer:

(-6p3) + (7p2q2) + (15pq)

Step-by-step explanation:

Perimeter of a rectangle = add all the sides.

In a rectangle, 2 of the sides will be equal.

So, if we have 4 sides, we will get 2 pairs of equal measurements.

Perimeter - (2 x the measurement of sides given) = (2 x the measurement of the other side.)

So...

(-22p3 + 32p2q2 + 16pq) - (2 x ( -6p3 + 7p2q2 + pq)) = (2 x the measurement of the other side.)

= (-22p3 + 32p2q2 + 16pq) - (-12p3 + 14p2q2 + 2pq) = (2 x the measurement of the other side.

So, first we group the like terms and change the signs accordingly.

So we get...

(-22p3 + 12p3) + (32p2q2 - 14p2q2) + (16pq - 2pq)

= (-10p3) + (18p2q2) + (14pq)

So, now all we have to do is do (- 22p3 + 32p2q2+ 16pq) - ( (-10p3) + (18p2q2) + (14pq))

= (-22p3 + 10p3) + (32p2q2 - 18p2q2) + (16pq + 14pq)

= ((-12p3) + (14p2q2) + (30pq) DIVIDED BY 2) = measurement of the other side.

Therefore, the measurement of the other side =

(-6p3) + (7p2q2) + (15pq)

Hope it helps :)