one leg of the right triangle is 10 cm and the hypotenuse is 20 cm longer than the other leg.Find the lenght of the unknown sides.

by Pythagoras

10^2 + x^2 = (20 + x)^2

x^2 + 100 = x^2 + 40x + 400

-300 = 40 x

there appears to be something wrong with the numbers in the problem

Let the unknown leg be x cm.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we can set up the equation:

x^2 + 10^2 = (x + 20)^2

Expand the equation:
x^2 + 100 = x^2 + 40x + 400

Simplify the equation:
100 = 40x + 400

Move 400 to the other side:
40x = -300

Divide both sides by 40:
x = -7.5

Since the length of a side cannot be negative, we can conclude that there is no such right triangle with these measurements.

Therefore, the lengths of the unknown sides cannot be determined.

To find the length of the unknown sides of the right triangle, let's denote the unknown leg as "x." Based on the given information, we can set up the following equation:

x^2 + 10^2 = (x + 20)^2

Let's solve this equation step by step:

1. Start by expanding the square on the right side:
x^2 + 100 = x^2 + 40x + 400

2. Subtract x^2 from both sides of the equation to eliminate the x^2 terms:
100 = 40x + 400

3. Next, subtract 400 from both sides:
40x = -300

4. Divide both sides by 40 to solve for x:
x = -300/40
= -7.5

Since length cannot be negative, we disregard the negative value. Therefore, the unknown leg of the right triangle is 7.5 cm.

To find the length of the hypotenuse, we substitute the value of x into the equation:

hypotenuse = x + 20
= 7.5 + 20
= 27.5 cm

Thus, the length of the unknown sides are:
Unknown leg: 7.5 cm
Hypotenuse: 27.5 cm