The length of the longer leg of a right triangle is 6 inches more than twice the length of the shorter leg. The length of the hypotenuse is 9 inches more than twice the length of the shorter leg. Find the side lengths of the triangle.​

9514 1404 393

  15 in, 36 in, 39 in

Step-by-step explanation:

The Pythagorean theorem tells us that for short side x, the relation is ...

  (2x +9)² = (2x +6)² +x²

  4x² +36x +81 = 4x² +24x +36 +x²

  x² -12x -45 = 0 . . . . . subtract the left-side expression

  (x -15)(x +3) = 0 . . . . factor

  x = 15 . . . . . . . . . . . the positive value of x that makes a factor zero

The side lengths of the triangle are 15 inches, 36 inches, and 39 inches.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.