Question 887877
PART of Right TRIANGLE:
short leg: x
long leg: x+7
hypotenuse: 2x+3

we can use Pythagorean thm: a^2 +b^2 = c^2
the a &b are the legs and the c is the hypotenuse of a right triangle.

x^2 + (x+7)^2 =(2x+3)^2
x^2 +x^2+14x+49 = 4x^2+12x +9
2x^2+14x+49=4x^2+12x=9
...........0= 2x^2 -2x -4-40
...........0=2(x^2 -x -20)
...........0=2(x-5)(x+4)
........... 0=2,0=x-5,0=x+4
solve for x: 0=2 not a solution because 0 does not equal 2
...........:x=5 can be a solution
...........:x=-4 not a solution because cannot have a negative length
so..
the shortest leg length is 5 cm

long leg:
x+7
5+7
12 cm

hypotenuse:
2x+3
2(5)+3
10+3
13 cm

ANSWER: short leg: 5cm
long leg: 12cm
hypotenuse: 13 cm

use Pythagorean thm to check if it this is the correct solution