Question

the distance of a chord by joining the mid points of the adjacent sides of a rectangle of the sides 10cm and 8 cm is​

Answer 1

Step-by-step explanation:

ANSWER

We know that diagonals of a rectangle are congruent. 

∴AC=BD

Join points AC (diagonal)

Consider ΔABC

Since P and Q are midpoints of the two sides of the triangle,

we can say that PQ∣∣AC and PQ=21AC        ..(i)

The segment joining midpoints of any 2 sides of a triangle is parallel to the 3rd side and is half of it

Similarly in ΔADC, RS∥AC and RS=21AC      ..(ii)

From (i) and (ii),  PQ=RS

Similarly, if we join BD (diagonal), we can prove that PS=QR

Since the diagonals of rectangle are equal in length, we can say PQ=RS=PS=QR

Thus, PQRS is a rhombus

Area of rhombus =21×product of diagonals

=21×QS×PR

=21×8×6=24 cm2