In obtuse-angled triangle ABC, the length of its longest side AB is 50 cm and one of the other two sides is 42 cm. If the area of the triangle is 294 cm2, what is the length (in cm) of its third side?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. .
Area = (1/2) × Base × Height
⇒ (1/2) × 42 × AD = 294
⇒ AD = 294/21 = 14 cm
In ΔADB, BD = √(AB2 - AD2) = √(502 - 142) = √(2500 - 196) = √2304 = 48 cm
CD = 48 - 42 = 6 cm
In ΔADC, AC = √(CD2 + AD2) = √(62 + 142) = √(36 + 196) = √232 = 2√58 cm
Therefore, the length of the third side is 2√58 cm.