55 ! the hypotenuse of a right triangle is 5cm more than 4 times the length of the shortest leg. the longer leg and the hypotenuse are consecutive integers. find all lengths.

Short leg is 9.

Hypotenuse is  41.

Long leg is 40.

Step-by-step explanation:

Shortest leg  is x.

Hypotenuse is (4x + 5).

Longer leg is shorter than hypotenuse, and they are consecutive numbers,

so longer leg is (4x + 5 - 1) = (4x + 4).

Using Pythagorean theorem

x² + (4x + 4)² = (4x + 5)²

x² + 16x² + 2*4x*4 + 4² = 16x² + 2*4x*5 + 5²

x² + 32x + 16 = 40x + 25

(x - 4)² = 5²

x - 4 = 5 or  x - 4 = - 5

x = 9 , or x = - 1

Leg cannot be negative.

So, short leg is 9.

Hypotenuse (4x+5) = (4*9 + 5) = 41

Long leg is 41 - 1 = 40

Check:

9² + 40² = 41²

1681 = 1681 True