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Question

ABC is a right angled triangle with B=90o, m is the midpoint of AC and Bm=117cm, AB+BC=30, then the area of the triangle is ____________?

A
108 cm2
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B
248 cm2
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C
316 cm2
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D
156 cm2
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Solution

The correct option is A 108 cm2
We know the length og median through B, Bm=12×2AB2+2BC2AC2
But by Pythoras theorem, AB2+BC2=AC2
Bm=AC2
AC2=4×117=468
Now AB+BC=30
So, (AB+BC)2=900
AB2+AC2+2AB×AC=900
AB×AC=(900AC2)×12=216
In ABC, area=12×AC×BC=108
So, Option (A)


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