Question

18) In ABC, ZACB = 90°, seg CD I seg AB. Also AD = 3 and BD = 9. Find the value of y. *​

Answer 1

Step-by-step explanation:

We have,

ABC is a right angle triangle.

In which ∠ACB=90⁰

And CD⊥AB and DE⊥AB Where D is any point in AB and E is any point in CB.

Prove that:- CD²×AC=AD×AB×DE

Proof:-

In ΔACB and ΔADC

∠CAB≅∠DAC(Reflexive)

∠ACB≅∠ADC(Right angle)

Thus, By AA similarity.

Then,

ΔACB∼ΔADC

⇒AC/AD = AB/AC

⇒AC l²=AB×AD

Now, Similarly

ΔACB∼ΔCDB

Now,

In ΔCED and ΔCDB

∠ECD≅∠DCB(Reflexive)

∠CED≅∠CDB(Right angle)

By AA similarity.

ΔCED∼ΔCDB

From equation (3) and (4) to,

ΔACB∼ΔCED

By equation (1) and (5) to, we get,

ΔADC∼ΔCED

AC/CD = DC/ ED

CD² =AC×DE

From equation (2) to,

AC²=AB×AD

On multiplying both side by CD²and we get,

CD²×AC²=CD²×AB×AD

CD²×AC²=AC×DE×AB×AD

CD²×AC=DE×AB×AD

CD²×AC=AD×AB×DE

Hence proved.