Question

Don't assume any length/angle unless specified
find the value of x​

Answer 1

Step-by-step explanation:

Given -

Figure

AB = 3 cm

BC = 3 cm

CD = 4 cm

ED = 5 cm

To Find -

Value of x.

Construction -

Join BD

Draw a line EF parallel to AB

Join DF

Now,

Here we see that AEFB is a rectangle

As we know that,

• Opposite sides of rectangle is equal

So,

EF = 3 cm

BD + DF = BF = x cm

Now,

In ΔBCD,

(BD)² = (BC)² + (CD)²

(BD)² = (3)² + (4)²

(BD)² = 9 + 16

(BD)² = 25

BD = √25

• BD = 5 cm

Now,

In ΔDEF,

(ED)² = (DF)² + (EF)²

(5)² - (3)² = (DF)²

25 - 9 = (DF)²

16 = (DF)²

DF = √16

• DF = 4 cm

So,

BF = BD + DF = x cm

= 5 + 4

= 9 cm

Hence,

The value of x is 9 cm.

Note -

ΔBCD and ΔDEF is a right-angle triangle.

Formula Used -

Pythagoras Theorem -

(Hypotenuse)² = (Perpendicular)² + (Base)²