ABC is a right angle triangle with B = 90. M is the mid point of AC and BM =root of 117 cm. Sum of the lengths of sides AB and BC is 30 cm. Find the area of the triangle ABC
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Answered by
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Take AB = c BC = a CA = b. Now the basic thing is midpoint of hypotenuse is circumcentre i.e. M then AM = BM = CM which is b/2=√117 then b²=4(117). Here area of triangle is ac/2 and we are given a+c=30 and a²+c²=b²=4(117) then ( a+c )²=900=4(225) then a²+c²+2ac=4(225). Hence 2ac=4(108) then area ac/2=108
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Answer:
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Step-by-step explanation:
Take AB = c BC = a CA = b. Now the basic thing is midpoint of hypotenuse is circumcentre i.e. M then AM = BM = CM which is b/2=√117 then b²=4(117). Here area of triangle is ac/2 and we are given a+c=30 and a²+c²=b²=4(117) then ( a+c )²=900=4(225) then a²+c²+2ac=4(225). Hence 2ac=4(108) then area ac/2=108
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