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
8 cm and 15 cm
Explanation:
Using the Pythagorean theorem we know that any right triangle with sides a, b and c the hypotenuse:
obviously the length of a side cannot be negative so the unknown sides are:
and
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#