Find the area of a triangle with perimeter 22cm, one side 9cm and difference of other two sides is 7cm using heron's formula.
Class 9
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Let, the sides be a = 9 cm, b and c.
a+b+c = 22
9+b+c = 22
b+c = 13
b-c = 7 (given)
by method of elimination,
we get, b = 10cm and c = 3cm.
now, semi-perimeter = 22/2 = 11
ar(triangle) = √ s (s-a) (s-b) (s-c)
= √ 11 (11-9) (11-10) (11-3)
= √ 11 × 2 × 1 × 4
= 2√22 cm²
a+b+c = 22
9+b+c = 22
b+c = 13
b-c = 7 (given)
by method of elimination,
we get, b = 10cm and c = 3cm.
now, semi-perimeter = 22/2 = 11
ar(triangle) = √ s (s-a) (s-b) (s-c)
= √ 11 (11-9) (11-10) (11-3)
= √ 11 × 2 × 1 × 4
= 2√22 cm²
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