Question

The side of a rhombus is 5 cm. If length of one diagonal of the rhombus is 8 cm, then find the length of the other diagonal.

Answer 1

area=4s
4(5)=20cm
area=1/2 ×d1×d2
20=1/2 ×8×d2
20=8d2/2
20=4d2
d2=20/4
d2=5cm is answer obtained

Answer 2

The diagonals of a rhombus intersect at right angle.

⇒ half of each diagonal and the length of the side will form a right angle triangle

Find 1/2 of the known diagonal:

Diagonal = 8 cm

1/2 the diagonal = 8 ÷ 2 = 4 cm

Find half of the other diagonal:

a² + b²  = c²

a² + 4² = 5²

a² = 5² - 4²

a² = 9

a = √9

a = 3 cm

Find the length of the diagonal:

1/2 the diagonal = 3 cm

the diagonal = 3 x 2 = 6 cm

Answer: The length of the other diagonal is 6 cm