Question

6. Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm
If one of its diagonals is 8 cm long, find the length of the other diagonal.​

Answer 1

Answer:

Since a rhombus is a parallelogram,

Area of rhombus = area of

parallelogram

=base×height

= 5cm×4.8cm

=24cm²

Now, area of rhombus = 24 cm²

=(1/2)×diagonal 1×diagonal 2=24

=(1/2)× 8cm× diagonal 2 = 24cm²

= diagonal 2= (24cm²×2)/8cm

= diagonal 2 = 6cm

Thus, the length of the other diagonal is 6cm.

Answer 2

Since,a rhombus is also a kind of a parallelogram.

Formula of area of rhombus =Base×Altitude

Putting values, we have

Area of rhombus =5×4.8=24

Since, Area of rhombus is 24 cm².

Also,formula for area of rhombus =$\frac{1}{2}×d_1d_2$

Given,Length of one diagonal =$d_1$=8

Let length of other diagonal =$d_2$

After substituting the values, we get

$24=\frac{1}{2}×8×d_2$

$24=4×d_2$

$4×d_2=24$

$d_2=\frac{24}{4}$

$d_2=6$

Hence, length of other diagonal is 6 cm.