the adjacent side of a parallelogram are 8cm and 6cm and it area is 48cm square. find the length of it diagonal.
Answers
Answered by
1
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
Similar questions