A room is in the shape of a right triangle. The hypotenuse is 8 meters longer than the short leg and the long leg is 4 meters longer than the short leg. Find the length of each side. (ok, now how can it be done if I change each side to cm and km, then ft and yards?)
Julie,check your 2-20-11,4:09 post.
To find the lengths of each side of the right triangle, we can use the Pythagorean theorem. According to the problem, the hypotenuse is 8 meters longer than the short leg (let's call this x), while the long leg is 4 meters longer than the short leg.
Let's use variables to represent the lengths of each side. Let x be the length of the short leg, y be the length of the long leg, and z be the length of the hypotenuse.
Using the Pythagorean theorem, we have the following equation:
x^2 + y^2 = z^2
We also have two additional pieces of information:
1. The hypotenuse is 8 meters longer than the short leg:
z = x + 8
2. The long leg is 4 meters longer than the short leg:
y = x + 4
Now we can substitute the values of y and z into the equation:
x^2 + (x + 4)^2 = (x + 8)^2
Expanding and simplifying this equation, we get:
x^2 + x^2 + 8x + 16 = x^2 + 16x + 64
Combining like terms, we have:
x^2 - 8x - 48 = 0
Now we can solve this quadratic equation to find the value of x, which represents the length of the short leg. Once we find x, we can substitute it into y = x + 4 and z = x + 8 to find the lengths of the long leg and hypotenuse respectively.
To solve the quadratic equation, you can use various methods such as factoring, completing the square, or using the quadratic formula. Once you find x, you can substitute it into the equations y = x + 4 and z = x + 8 to find the respective lengths of the long leg and hypotenuse.
If you want to change the units of measurement to centimeters (cm), kilometers (km), feet (ft), or yards, you can simply convert the lengths accordingly.
For example, if you want to convert the lengths to centimeters, you would multiply them by 100 (since there are 100 centimeters in 1 meter). To convert to kilometers, you would divide them by 1000 (since there are 1000 meters in 1 kilometer). To convert to feet, you would multiply them by 3.28 (since there are 3.28 feet in 1 meter). And to convert to yards, you would divide them by 0.9144 (since there are 0.9144 meters in 1 yard).
The numerical answer would be the same if the information were given in cm, m, or feet.
Let x be the short side.
long side = x+4
hypotenuse = x+8
Apply Pythagoras theorem:
(x+4)²+x² = (x+8)²
Solve for x (it is a quadratic equation).
You will find two integer solutions, one of which is negative and should be rejected.