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