Question

Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.​

Answer 1

Step-by-step explanation:

Wehave

side=6cm

height=4cm

Areaofa∥gm=base×height

=6×4

=24cm

2

Areaofarhombus= 21 ×d 1 ×d 2

⇒24= 21 ×8×d 2

⇒d 2 = 824×2

∴d 2 =6

Hence,otherlengthis6cm.

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 =6×4=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.