Question

calculate x in the following figure.

please solve the full question.
and explain in the answer​

Answer 1

Answer:

16 cm

Step-by-step explanation:

As ∆ABC is a right angled triangle, so by using Pythagoras property,

• BC = Base
• AB = Hypotenuse = 55 cm
• AC = Perpendicular = 44 cm

→ H² = B² + P²

→ AB² = BC² + AC²

→ AB² ― AC² = BC²

→ (55 cm)² ― (44 cm)² = BC²

→ 3025 cm² ― 1936 cm² = BC²

→ 1089 cm² = BC²

→ √(1089 cm²) = BC

→ 33 cm = BC⠀⠀⠀⠀⠀⠀⠀⠀… ( 1 )

Now, In ∆BCD :

• BC = Perpendicular = 33 cm (Found above)
• BD = Base = 56 cm
• CD = Hypotenuse

By using Pythagoras property,

→ H² = B² + P²

→ CD² = BD² + BC²

→ CD² = (56 cm)² + (33 cm)²

→ CD² = 3136 cm² + 1089 cm²

→ 4225 cm² = CD²

→ √(4225 cm²) = CD

→ 65 cm = CD⠀⠀⠀⠀⠀⠀⠀⠀… ( 2 )

Now, in ∆CDE :

• CD = Hypotenuse = 65 cm (Found above)
• DE = Base = 63 cm
• CE = Perpendicular = x

→ H² = B² + P²

→ CD² = DE² + CE²

→ CD² ― DE² = CE²

→ (65 cm)² ― (63 cm)² = CE²

→ 4225 cm² ― 3969 cm² = CE²

→ 256 cm² = CE²

→ √(256 cm²) = CE

→ 16 cm = CE

Therefore, the value of x is 16 cm. $\;$

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Answer 2

GIVEN :-

a figure

to calculate :-

value of x = ?

SOLUTION :-

In ∆ ABC by pythagoras theorem

BC = √(AB) ^ 2 - ( Ac) ^ 2)

BC = √ (55) ^ 2 - (44) ^ 2

BC = √ 3025 - 1936

BC = √1089 = 33 cm

IN ∆ BCE by pythagoras theorem:-

EC = √(BE) ^ 2 + (BC) ^ 2)

EC = √(56) ^ 2 + (33) ^ 2)

EC = √ 3136 + 1089

EC = √ 4225 = 65 cm

IN ∆ EDC :-

(CD) = √ (CE) ^ 2 - (ED) ^ 2)

x = √(65) ^ 2 - (63) ^ 2)

x = √ 4225 - 3969

x = √ 256 = 16 cm

Hence the value of x is 16cm is the

answer.