Question

The hypotenuse of a right triangle is five centimeters longer than one leg and 10 centimeters longer than the other leg. What are the dimensions of the triangle?

Answer 1

Answer:

20 is one leg, 25 is the hypotenus, and finally 15 is the last leg.

Step-by-step explanation:

We can confirm this by using the following strategy. Adding the two legs to see if they are bigger than the hypotenuse. If this is so the information is valid of not it is wrong in this case this strategy works.

Answer 2

Answer:

15, 20, and 25

Step-by-step explanation:

Let's call the shortest leg of the triangle x. By the Pythagorean Theorem:

$\sqrt{x^2+(x+5)^2}=x+10$

Square both sides:

$x^2+(x+5)^2=(x+10)^2$

Expand parentheses:

$x^2+x^2+10x+25=x^2+20x+100$

Simplify:

$2x^2+10x+25=x^2+20x+100 \\\\x^2-10x-75=0$

Factor:

$(x-15)(x+5)=0$

By the zero product rule, x=15, and therefore the other two legs are 20 and 25. Hope this helps!