Question

s a f e is a rhombus as shown in figure 7 find X Y and Z justify your findings​

Answer 1

Step-by-step explanation:

Given :-

SAFE is a Rhombus and OA = 12 cm and OF=9cm

To find :-

Find the values of x,y and z and justify your answers ?

Solution :-

Given that :

SAFE is a rhombus

OA = 12 cm

OF = 9 cm

AE and SF are two diagonals of the rhombus

We know that

In a rhombus, The diagonals bisect each other.

=> AE = AO + OE

=> AE = 2AO = 2OE

=> AO = OE = AE/2

The value of OE =OA = 9 cm

y = 12 cm

and

SO + OF = SF

=> SF = 2 SO = 2 OF

=> SO = OF = SF/2

The value of SO = OF = 9 cm

x = 9 cm

Now ,

We know that

Diagonals bisect each other at right angle

So , ∆ ASO is a right angled triangle

By Pythagoras theorem

Hypotenuse² = Side² + Side²

=> AS² = AO² + SO²

=> AS² = 12²+9²

=> AS² = 144+81

=> AS² = 225

=> AS = ±√225

=> AS = ±15

Since AC can not be negative.

AS = 15 cm

We know that

All sides are equal in a rhombus

=> AS = SE = EF = FA = 15 cm

z = 15 cm

Answer:-

The value of x = 9 cm

The value of y = 12 cm

The value of z = 15 cm

Used formulae:-

In a rhombus ,

• All sides are equal.

• Digonals bisect each other.

• Diagonals bisect perpendicular bisect each other.

Answer 2

Answer:

x= 9cm ( alternate interior angles are always same)

y= 12 cm ( alternate interior angles are always same)

z= OE²+ OF² = EF

144+81= 225

z= 15 cm