Question

In Fig ABCD is a rectangle P and Q are midpoints of AD and DC respectively. Then length of PQ is:

Answer 1

Answer:

2.5 cm

Step-by-step explanation:

here ac = 5 cm by Pythagoras  theorem

then dp is 1.5 (since it is mid point of 3 cm long ad)

similarly dq = 2 again by pythagoras theorem PQ  = 2.5 cm

Answer 2

Given,

ABCD is a rectangle.

P and Q are the midpoints of AD and DC respectively.

AB = 4 cm

BC = 3 cm

To find,

The length of PQ.

Solution,

The length of PQ will be 2.5 cm.

We can easily solve this problem by following the given steps.

We know that in a rectangle the opposite sides are of equal length and all four angles are right angles (90°).

So, AB = DC = 4 cm

BC = AD = 3 cm

According to the question,

P and Q are the midpoints of AD and DC respectively.

So, PD = AD/2 = 1.5 cm

DQ = DC/2 = 2 cm

∆ PDQ is a right-angled triangle.

Using the Pythagoras theorem in ∆ PDQ,

PQ² = PD² + DQ²

PQ² = (1.5)² + (2)²

PQ² = 2.25 + 4

PQ² = 6.25

PQ = √6.25

PQ = 2.5 cm ( The square root of 625 is 25 and that of 100 is 10. So, the square root of 6.25 is 2.5.)

Hence, the length of PQ is 2.5 cm.