Question

fine the area of a triangle two side of which are 18cm and 10cm perimeters is 42cm

Answer 1

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HERE IS YOUR ANSWER :-



The two sides are 18 cm and 10 cm.



Perimeter of triangle is 42 cm.



Let the third side be " x cm ".



Perimeter of triangle = 18 + 10 + x



42 = 28 + x



x = 42 - 28



x = 14 cm .



So the third side of triangle is 14 cm.



Let



a = 18 cm


b = 10 cm.


c = 14 cm.





$s = \frac{a + b + c}{2} \\ \\ \\ = \frac{18 + 10 + 14}{2} \\ \\ \\ = \frac{42}{2} \\ \\ \\ = 21 \\ \\ \\ by \: herons \: formula \\ \\ \\ area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - a)} \\ \\ \\ = \sqrt{21(21 - 18)(21 - 10)(21 - 14)} \\ \\ \\ = \sqrt{7 \times 3 \times 3 \times 11 \times 7} \\ \\ \\ = 7 \times 3 \sqrt{11} \\ \\ \\ = 21 \sqrt{11}$