Question

In ∆ABC, m∠ABC = 90° and seg BD ⊥ side AC. AD = 18 and DC = 8 then, find the values of BD and AB.

Answer 1

Given :-

• In ∆ABC, m∠ABC = 90°.
• seg BD ⊥ side AC.
• AD = 18 , DC = 8

To Find :-

• The values of BD and AB.

Solution :-

Condition (1) :-

In ∆ABC, seg BD ⊥ side AC .

According to Geometric mean theorem,

↪BD² = AD × DC

↪BD² = 18 × 8

↪ BD² = 144

↪ BD = √144

↪ ${\boxed{\sf{\red{BD = 12}}}}$

Condition (2) :-

In ∆ABD , m∠ABD= 90°.

According to Pythagoras theorem,

↪ AD² = AB² + BD²

↪ 18² = AB² + 12²

↪ AB² = 18² - 12²

↪AB² = (18 - 12) × (18 + 12)

↪ AB² = 180

↪ AB = √180

↪ ${\boxed{\sf{\blue{AB = 6√5}}}}$

Hence,

• The values of BD and AB is 12 and 6√5.

Answer 2

Answer:

ɢɪᴠᴇɴ :-

ɪɴ ∆ᴀʙᴄ, ᴍ∠ᴀʙᴄ = °.

sᴇɢ ʙᴅ ⊥ sɪᴅᴇ ᴀᴄ.

ᴀᴅ = , ᴅᴄ =

ᴛᴏ ғɪɴᴅ :-

ᴛʜᴇ ᴠᴀʟᴜᴇs ᴏғ ʙᴅ ᴀɴᴅ ᴀʙ.

sᴏʟᴜᴛɪᴏɴ :-

ᴄᴏɴᴅɪᴛɪᴏɴ () :-

ɪɴ ∆ᴀʙᴄ, sᴇɢ ʙᴅ ⊥ sɪᴅᴇ ᴀᴄ .

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ɢᴇᴏᴍᴇᴛʀɪᴄ ᴍᴇᴀɴ ᴛʜᴇᴏʀᴇᴍ,

↪ʙᴅ² = ᴀᴅ × ᴅᴄ

↪ʙᴅ² = ×

↪ ʙᴅ² =

↪ ʙᴅ = √

↪ {\ʙᴏxᴇᴅ{\sғ{\ʀᴇᴅ{ʙᴅ = }}}}

ʙᴅ=

ᴄᴏɴᴅɪᴛɪᴏɴ () :-

ɪɴ ∆ᴀʙᴅ , ᴍ∠ᴀʙᴅ= °.

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴘʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ,

↪ ᴀᴅ² = ᴀʙ² + ʙᴅ²

↪ ² = ᴀʙ² + ²

↪ ᴀʙ² = ² - ²

↪ᴀʙ² = ( - ) × ( + )

↪ ᴀʙ² =

↪ ᴀʙ = √

↪ {\ʙᴏxᴇᴅ{\sғ{\ʙʟᴜᴇ{ᴀʙ = √}}}}

ᴀʙ=√

ʜᴇɴᴄᴇ,

ᴛʜᴇ ᴠᴀʟᴜᴇs ᴏғ ʙᴅ ᴀɴᴅ ᴀʙ ɪs ᴀɴᴅ √.

Step-by-step explanation:

ᴛʜɪs ɪs ʏᴏᴜʀ ᴀɴsᴡᴇʀ ᴘʟᴢ ғᴏʟʟᴏᴡ ᴍᴇ