Question

explain with all the steps.

the diagonals of a rhombus are 30 cm and 16cm. find the length of sides and perimeter.

Answer 1

Answer:

Step-by-step explanation:

Let ABCD is a rhombus

AB,BC,CD,AD are the sides of the rhombus and

AC and BD are the diagonals of the rhombus

Where

AC= 30

BD=16

and o is the point where daigonals are bisect each other

As we know the property of rhombus that daigonals are bisect each other then

AO=CO=15

BO=OD=8

Since diagonals are perpendicular to each other then we can apply Pythagoras theoram on it

By applying Pythagoras theoram on ∆AOD

AD^2=A0^2+OD^2

AD^2=15^2+8^2

AD^2=289

AD=17

Since all the sides of the rhoumbus are congruent

Hence of the side of the rhoumbus is 17cm

Answer 2

Hi friend!

Answer:

We know that diagonals of a rhombus bisect at 90°.
So they would form 4 right-angled triangles inside the rhombus.

Now, what will be the lengths of the sides that become the base and height of each triangle?
It will be half the length of each diagonal respectively.

Ok, so we got the sides of the triangle.
They're 15cm & 8cm.

Formula for finding hypotenuse:
Pythagoras stated and proved that—
a² + b² = c²
where a and b are base and height, and c is the hypotenuse.
a = 15
b = 8
c = ?

15² + 8² = c²
225 + 64 = c²
c² = 289
c = √289
c = 17

Now that we got the side of the rhombus, 17cm, let's move on to find the perimeter and area of the rhombus.

Perimeter = 4 × side
= 4 × 17 = 68cm

Area (rhombus) = ½ × d1 × d2
= ½ × 30 × 16
= 240cm²

Therefore, Perimeter of the rhombus = 68cm
Area = 240cm²

Hope you found my answer helpful. Keep Smiling!