Question

two adjacent sides of a parallelogram are 8cm and 6cm and its area is 48cm².find the length of its diagonal

Answer 1

Answer:

10 cm long

Step-by-step explanation:

Since 8*6 = 48 => one of the sides is the height as area parallelogram = Base * Height! This indicates the shape is really a rectangle. But let us see if this can be proved.

Consider any one diagonal which bisects the parallelogram into 2 equal halves.

The area of the triangle with the two adjacent sides and the diagonal

= 48/2 = 24 sq. cm

Area of this triangle = 1/2 absinC = 24

1/2 * 6 * 8 * SINC = 24

24 * SIN C = 24

SIN C = 1

C = 90 Degrees

This indicates that the said parallelogram is a rectangle and both diagonals are the same length

Diagonal length = sqrt(6² + 8²) = sqrt(36 + 64) = sqrt (100) = 10cm

Both Diagonals are 10cm long