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Question

Triangle abc ab=ac=x bc=10cm area=60cm2


Solution

Area = 60 cm^2
Firstly, find out area of the triangle ABC, from Heron's Formula.
Semi perimeter (s)= (x+x+10)/2=x+5 cm
Area =√ s(s−x)(s−x)(s−10)
60= √(x+5)(x+5−x)(x+5−x)(x+5−10)
60= √25(x+5)(x−5)
60= √25(x^2−5^2)
Squaring both sides,
3600= 25(x^2−25)
144+25=x^2
169=x^2
±13=x
Since, side cannot be negative, therefore value of x is equal to 13 cm.

Mathematics

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