A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30 meters longer than the length of the longer leg. How long is the longer leg?
L=longer leg
By Pythagoras theorem:
90²+L²=(L+30)²
Solve for L.
8100+L²=L²+60L+900
To find the length of the longer leg in a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
Let's represent the length of the longer leg as x. We are given that the shorter leg measures 90 meters and the hypotenuse is 30 meters longer than the longer leg.
So, the two legs can be represented by x and 90 meters, and the hypotenuse can be represented by (x + 30) meters.
According to the Pythagorean theorem, we have:
x^2 + 90^2 = (x + 30)^2
Expanding this equation, we get:
x^2 + 8100 = x^2 + 60x + 900
Rearranging the equation, we have:
x^2 - x^2 + 60x = 900 - 8100
Combining like terms, we get:
60x = -7200
Dividing both sides of the equation by 60, we find:
x = -120
The length of the longer leg cannot be negative, so it must be a mistake in the question. Please double-check the given information for correctness.
To find the length of the longer leg of the right triangle, we need to understand the relationship between the three sides: the shorter leg, the longer leg, and the hypotenuse.
Let's denote the shorter leg as "a," the longer leg as "b," and the hypotenuse as "c." We know that the shorter leg measures 90 meters, so a = 90.
The problem also tells us that the hypotenuse (c) is 30 meters longer than the length of the longer leg (b). So, we can express this as c = b + 30.
Now, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as:
a^2 + b^2 = c^2
Substituting the given values, we have:
90^2 + b^2 = (b + 30)^2
Expanding the equation, we get:
8100 + b^2 = b^2 + 60b + 900
We can simplify it by subtracting b^2 from both sides:
8100 = 60b + 900
Next, we isolate the term with "b" by subtracting 900 from both sides:
7200 = 60b
Finally, we can solve for "b" by dividing both sides by 60:
b = 120
Therefore, the longer leg of the right triangle measures 120 meters.