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 8cm long, find the length of the other diagonal.
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Answer 1

Step-by-step explanation:

Here,

side = 5cm

height= 4.8cm

therefore area of a rhombus = base(or side)× height

= 5cm × 4.8cm

= 24cm²

given ,

diagonal = 8cm

let the other diagonal be d(2)

therefore ,

area of a rhombus = d(1)×d(2) /2

24cm² = 8cm ×d(2)/2

24cm² = 4cm× d(2)

24cm²/4cm = d(2)

d(2) = 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.