Hypotenuse of a right triangle is 25 , cm and | vedclass

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Question

(A) Let one side be $x \, cm$. Then the other side will be $(x+5) \, cm$.According to the Pythagoras Theorem:$x^{2} + (x+5)^{2} = (25)^{2}$Expanding t

Vedclass · Accepted Answer

$15 \, cm, 20 \, cm$

Vedclass · Answer

(A) Let one side be $x \, cm$. Then the other side will be $(x+5) \, cm$.According to the Pythagoras Theorem:$x^{2} + (x+5)^{2} = (25)^{2}$Expanding the equation:$x^{2} + x^{2} + 10x + 25 = 625$$2x^{2} + 10x - 600 = 0$Dividing by $2$:$x^{2} + 5x - 300 = 0$Factoring the quadratic equation:$x^{2} + 20x - 15x - 300 = 0$$x(x+20) - 15(x+20) = 0$$(x-15)(x+20) = 0$Thus,$x = 15$ or $x = -20$.Since the length cannot be negative,we reject $x = -20$.Therefore,one side is $15 \, cm$ and the other side is $15 + 5 = 20 \, cm$.

Hypotenuse of a right triangle is $25 \, cm$ and out of the remaining two sides,one is longer than the other by $5 \, cm$. Find the lengths of the other two sides.

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