Question

a right triangles longer leg is 2 inches more than twice the shorter leg, and the hypotenuse is 1 inch more than the longer leg. find the dimensions of the right triangle​

Answer 1

Answer: 5;12;13

Step-by-step explanation:

let's call the shortest leg

$x$

and then the longer leg and the hypotenuse

$2x + 2$

$2x + 3$

respectively, and then apply pythagorean theorem to the triangle:

$x^2+(2x+2)^2=(2x+3)^2$ at this point is simple number crunching;

$x^2+4x^2+8x+4=4x^2+12x+9 \\ x^2-4x-5=0 \rightarrow (x-5)(x+1)=0$

the only valid solution is obviously x=5 since its a length of a segment.