The length of the base of isosceles triangle is 24 cm and the length of the leg is 20 cm. Determine the ratio in which center of the inscribed circle divides the altitude on the base.PLEASE ANSWER THIS QUESTION.I WILL MARK THEM AS BRAINLIEST.
Answers
Given :- The length of the base of isosceles triangle is 24 cm and the length of the leg is 20 cm.
To Find :- Determine the ratio in which center of the inscribed circle divides the altitude on the base. ?
Answer :-
Since, the altitude of an isosceles triangle bisects the base .
so, using pythagoras theorem we get,
→ Altitude = √[(equal side)² - (Base/2)²]
→ Altitude = √[(20)² - (12)²]
→ Altitude = √(400 - 144)
→ Altitude = √(256)
→ Altitude = 16 cm .
now, if we assume a as equal sides and b as base ,
→ Inradius = (b/2)√[(2a - b)/(2a + b)]
→ Inradius = (24/2)√[(2*20 - 24)/(2*20 + 24)]
→ Inradius = 12√(16/64)
→ Inradius = 12 * (1/4)
→ Inradius = 3 cm .
therefore,
→ Length of Altitude left after inradius = 16 - 3 = 13 cm .
hence, center of the inscribed circle divides the altitude on the base in the ration 13 : 3.
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Answer:
answer is correct 3:5 .
above explanation is correct but whare 1/4 is replace by 1/2