Question

find the area of a triangle two sides of which are 18 and 12 and perimeter is 48cm. solve the sum using herons formula

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Answer 1

Answer:

Perimeter= 48cm

missing side= 48-(18+12)=48-30=18cm

Now, Semi perimeter= 48/2=24cm

$\sf Area ~ of ~triangle= \sqrt{s(s-a)(s-b)(s-c)} \\\\\sf= \sqrt{24(24-18)(24-12)(24-18)} \\\\\sf=\sqrt{24(6)(12)(6)} \\\\\sf=\sqrt{24x36x12} \\\\\sf=\sqrt{2x2x2x3x3x2x3x2x3x2x2} \\\\\sf=\sqrt{2x2x2x2x2x2x2x3x3x3x3} \\\\\sf=72\sqrt{2} \\\\\sf=101.82cm^2\\\\\\\setlength{\unitlength}{1cm}\begin{picture}(6,6) \put(2, 2){\line(0, 1){2}} \put(2, 4){\line(1, 0){4}}\\\put(2, 2){\line(2, 1){4}}\end{picture}$