Question

The perimeter of the rhombus is 40cm . if one diaogn is 16cm find its another diagonal and area

Answer 1

perimeter is 40 so
each side will be 40/4=10cm
now imagine a rhombus
half of D1 is 16/2=8
in that triangle use Pythagoras thm
we get
10*10=8*8+X*X
100=64+X*X
X*X=100-64
X*X=36
so X=6
so the another diagonal is 6*2=12cm
area of rhombus is
1/2*D1*D2
1/2*16*12
1/2*192
96
so area of rhombus is 96sqcm

Answer 2

Answer:

• Length of other diagonal = 12 cm.

• Area of the Rhombus = 96 cm².

Step by step explanation:

[ Refer the attachment for figure. ]

Perimeter of Rhombus = 40 cm.

» Side = 1/4 × 40 = 10 cm.

One diagonal = 16 cm.

Diagonals of Rhombus bisect each other at right angles.

Now,

OB = √ (AB² - OA²)

= √ ( 10² - 8² )

= √ ( 100 - 64 )

= √ 36

= 6 cm.

Thus, Diagonal BD = 6 × 2 = 12 cm.

Now, Area of Rhombus = 1/2 × Product of diagonals

= 1/2 × 12 × 16

= 1/2 × 192

= 96 cm²

Hence, Area of Rhombus is 96 cm².

Final answers:

Length of other diagonal = 12 cm.

Area of the Rhombus = 96 cm².