Question

the perimeter of a right angle triangle is 30cm and its hypotenuse is 13cm .Find the other two sides.​

Answer 1

Answer:

Other two sides are 12,5

Step-by-step explanation:

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Answer 2

$Let \: x\: and \: y \: are \: two \: perpendicular$

$sides \: of \: a\: right \: angle \: triangle$

$Hypotenuse (h) = 13 \: cm$

$Perimeter = 30 \: cm \: ( given )$

$\implies x + y + h = 30$

$\implies x + y = 30 - h$

$\implies x + y = 30 - 13$

$\implies x + y = 17$

$\implies y = 17 - x \: --(1)$

/* By Phythagorean theorem */

$x^{2} + y^{2} = 13^{2}$

$\implies x^{2} + (17-x)^{2} - 13^{2} = 0$

$\implies x^{2} + 289 + x^{2} - 34x - 169 = 0$

$\implies 2x^{2} -34x + 120 = 0$

$\implies x^{2} -17x + 60 = 0$

$\implies x^{2} -12x - 5x + 60 = 0$

$\implies x(x-12) - 5(x-12)=0$

$\implies (x-12)(x-5)= 0$

$\implies x-12= 0 \: Or \: x-5= 0$

$\implies x = 12 \: Or \: x = 5$

/* Put values of x in equation (1), we get */

$i) If \: x = 12 \: then \: y = 17 - 12 = 5$

$ii) If \: x = 5 \: then \: y = 17 - 5 = 12$

Therefore.,

$\green {5 \: and \: 12 \: are \: other \: two \: sides \: of }$

$\green { sides \: of \: right \: triangle . }$

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