Question

the perimeter of rhombus is 40cm and the distance between a pair of parallel sides is 5.6 cm if the length of one of its diogonal is 7 cm find the length of the other diogonal

Answer 1

hiii!!!

here's ur answer...

given the height ( distance between the parallel sides ) of the rhombus is 5.6cm.

perimeter of the rhombus = 40cm

therefore side × 4 = 40cm

==> side = 40/4

==> side = 10cm

VERIFICATION :-

perimeter of the rhombus = side × 4

= 10 × 4

= 40cm

hence verified

thus the side of the rhombus is 10cm.

now,

to find the area of a rhombus, we have to formulas. one is 1/2 × d1 × d2. in this both diagonals are given. second one is b × h. as we know rhombus is also a parallelogram. base is the side of the rhombus and height is the perpendicular distance.

base = 10cm

height = 5.6cm

area of the rhombus = b × h

= 10 × 5.6

= 56cm²

given the Length of one diagonal is 7cm.

area of the rhombus = 56cm²

therefore 1/2 × d1 × d2 = 56cm²

==> 1/2 × 7 × d2 = 56cm²

==> 3.5 × d2 = 56cm²

==> d2 = 56/3.5

==> d2 = 16cm

VERIFICATION :-

area of the rhombus = 1/2 × d1 × d2

= 1/2 × 7 × 16

= 7 × 8

= 56cm²

hence verified

thus the another diagonal of the rhombus is 16cm.

hope this helps.!!

Answer 2

Hay
Dear user -

perimeter of the rhombus = 40cm

therefore side × 4 = 40cm

=> side = 40/4

=> side = 10cm

Then, the side of the rhombus is 10cm.

now,

We have find the area of a rhombus, we have to formulas. o 1/2 × d1 × d2.

base = 10cm

height = 5.6cm

Then,

area of the rhombus = b × h

= 10 × 5.6

= 56cm²

According to question given the Length of one diagonal is 7cm.

area of the rhombus = 56cm²

therefore 1/2 × d1 × d2 = 56cm²

=> 1/2 × 7 × d2 = 56cm²

=> 3.5 × d2 = 56cm²

==> d2 = 56/3.5

=> d2 = 16cm

Then


thus the another diagonal of the rhombus is 16cm.