The hypotenuse of a right triangle is 17 cm long. Another side of the triangle is 7 cm longer than the third side. How do you find the unknown side lengths?

2 Answers
Bill Jorgensen
Jun 2, 2018

8 cm and 15 cm

Explanation:

Using the Pythagorean theorem we know that any right triangle with sides a, b and c the hypotenuse:

#a^2 + b^2 = c^2#

#c=17#

#a = x#

#b = x+7#

#a^2 + b^2 = c^2#

#x^2 + (x+7)^2 = 17^2#

#x^2 + x^2 +14x + 49 = 289#

#2x^2 +14x = 240#

#x^2 +7x -120 = 0#

#(x + 15) (x - 8)=0#

#x=-15#

#x=8#

obviously the length of a side cannot be negative so the unknown sides are:

#8#

and

#8+7=15#

Jim G.
Jun 2, 2018

#8" and "15#

Explanation:

#"let the third side "=x#

#"then the other side "=x+7larrcolor(blue)"7 cm longer"#

#"using "color(blue)"Pythagoras' theorem"#

#"square on the hypotenuse "=" sum of squares of other sides"#

#(x+7)^2+x^2=17^2#

#x^2+14x+49+x^2=289#

#2x^2+14x-240=0larrcolor(blue)"in standard form"#

#"divide through by 2"#

#x^2+7x-120=0#

#"the factors of - 120 which sum to + 7 are + 15 and - 8"#

#(x+15)(x-8)=0#

#"equate each factor to zero and solve for x"#

#x+15=0rArrx=-15#

#x-8=0rArrx=8#

#x>0rArrx=8#

#"lengths of unknown sides are"#

#x=8" and "x+7=8+7=15#

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