Question

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?

Answer 1

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`

Answer 2

`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`