Question

7. The length of each side of a rhombus is 5 cm. If the length of one of its diagonals is 6 cm,
find the length of the other diagonal.
Construct a rectangle ABCD given that AB = 5 cm and diagonal AC = 7 cm.​

Answer 1

since the length of a side of a rhombus is square centimetre

when we draw Rhombus we will find that all the triangles in rhombus is making a right angle triangle

let's take one of them BOC

in triangle BOC,

by pythagoras theorem,

${h}^{2} = {p}^{2} + {b }^{2} \\ {5}^{2} = {p}^{2} + {3 }^{2} \\ 25 = {p}^{2} + 9 \\ p = \sqrt{25 - 9 } \\ p = \sqrt{16} \\ p = 4$

we have find that, OB = 4cm

then, BD=2×4

=8cm

Answer 2

Answer:

The diagonals of a rhombus intersect at the right angle.

half of each diagonal and the length of the side will form as a right-angle triangle.

Diagonal =8 cm.

2

1

of the diagonal =

2

8

=4 cm

∴a

2

+b

2

=c

2

⇒a

2

+4

2

=5

2

⇒a

2

−25=16

⇒a

2

=9

⇒a=

9

⇒a=3.

Length of the diagonal

2

1

of the diagonal =3 cm

the diagonal =3×2=6 cm

∴ The length of the other diagonal is 6 cm