Question

In rhombus PURE, PE = 3x cm and PU = 2(x+3) cm. Find the length of each side of the rhombus (answer me fast with step by step)​

Answer 1

Answer:

All the sides of a rhombus are equal so

3x cm = 2(x+3) cm

3x = 2x+6

3x - 2x = 6

x = 6

Hence all sides of the rhombus = 3 × x = 18cm

Answer 2

Given :

• First side (PE) = 3x
• Second Side (PU) = 2(x+3)

To Find :

The length of all the side of the rhombus .

Property To be used here :

We will use the one of the main properties of rhombus, The property Is :

• A rhombus is a parallelogram with all the sides equal
• Or we can say, A parallelogram with all side equal is a Rhombus

We will use this property of rhombus here to find the measurements of each side

Process :

From the property of rhombus stated above , we can say that the given sides are equal, so we will form an equation with this and solve that equation to get x, then we will find the length of each side.

I will also show you the verification.

Solution :

As stated Above, we get that :

Side PE = Side PU

$\tt{ \implies 3x = 2(x + 3)}$

$\implies \tt{3x = 2x + 6}$

$\implies \tt{3x - 2x = 6}$

$\red{ \underline{ \boxed{ \tt{ \therefore \: x = 6}}}}$

Hence, x = 6

So, the side = 18 cm

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Verification :

Now, we will check that if we have hot the correct value or not :

As we got the value of x as 6 , we will apply it on the two different side if the rhombus.

Let, 3x = RHS

2(x+3) = LHS

So, 3x = 3×6 = 18

And, 2(x+3) = 2(3+6) = 2(9) = 18

Hence, LHS = RHS ,

Hence, Verified !

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Additional Information :

These are some Quadrilateral, from higher level to lower level :

1] Quadrilateral: A polygon with 4 sides is called as Quadrilateral

2] Trapezium : A Quadrilateral which have atleast one pair of Parallel sides is called a trapezium

Kite : A Quadrilateral, which have atleast two pair of adjacent side equal .

3] Parallelogram: A Trapezium with opposite side equal and Parallel is called a Parallelogram. The diagonal bisect each other.

4] Rhombus : A parallelogram, Trapezium and A kite, which have all side equal to each other and the diagonals bisect each other at 90° is a rhombus.

5] Rectangle: A parallelogram, Trapezium , which have opposite side equal and Parallel . All the angles are 90° is called a Rectangle.

6] Square: A Trapezium,Kite, Rectangle, and A rhombus , which have all side equal, opposite side Parallel, and all the angles are 90°, diagonals are equal and bisect each other at 90°. This is called a Square.