The hypotenuse of an isosceles right angled triangle is 12 cm. Find its area.
Answers
Let ABC be the given triangle right angled at B with AB=BC — (1)
AREA OF TRIANGLE = 12CM^2
Area of triangle = 1/2bh
==》 1/2 × BC × AB = 12
==》1/2 × BC × BC = 12
==》1/2 × BC^2 = 12
BC^2 = 24
BC = 4.9CM (APPROX )
Length of the base= 4.9 cm (approx )
Hᴇʀᴇ's Yᴏᴜʀ Aɴsᴡᴇʀ:-
Lᴇᴛ ABC ʙᴇ ᴀ Rɪɢʜᴛ Aɴɢʟᴇᴅ Isᴏsᴄᴇʟᴇs Tʀɪᴀɴɢʟᴇ Wʜᴏsᴇ Hʏᴘᴏᴛᴇɴᴜsᴇ ɪs 12 ᴄᴍ ( AC ).
Bʏ Pʏᴛʜᴀɢᴏʀᴀs Tʜᴇᴏʀᴀᴍ,
AC² = AB² + BC²
AB = BC ( ABC ɪs ᴀɴ Isᴏsᴄᴇʟᴇs Tʀɪᴀɴɢʟᴇ )
AB² = BC²
AC² = AB² + BC²
AC² = AB² + AB²
(12ᴄᴍ)² = 2AB²
144ᴄᴍ² = 2AB²
AB² = 144ᴄᴍ²/2
AB² = 72ᴄᴍ²
AB = √72ᴄᴍ²
AB = 6√2ᴄᴍ
Tʜᴇʀᴇғᴏʀᴇ, BC = 6√2ᴄᴍ
Aʀᴇᴀ ᴏғ Tʜᴇ Tʀɪᴀɴɢʟᴇ = ½ × AB × BC
= ½ × 6√2 × 6√2
= ½ × 72ᴄᴍ²
= 36ᴄᴍ²
Tʜᴇʀᴇғᴏʀᴇ, Tʜᴇ Aʀᴇᴀ ᴏғ Tʀɪᴀɴɢʟᴇ ɪs 36ᴄᴍ².
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