To repair a roof that is 4 meters high, Mr. Russo leans a 5-meter ladder against the side of the building. To reach the roof, how far away from the building should he place the base of the ladder?
x^2 + 4^2 = 5^2
x = 3
You should make a point to memorize the right-angled triangle with sides
3-4-5 as the smallest right-angled triangle with integer sides
To determine how far away from the building Mr. Russo should place the base of the ladder, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the other two sides.
In this case, one side of the right triangle is the height of the roof, which is 4 meters. The other side is the distance from the base of the ladder to the building, which we'll call "x." The hypotenuse is the length of the ladder, which is 5 meters.
Using the Pythagorean theorem, we can set up the following equation:
x^2 + 4^2 = 5^2
Simplifying this equation, we have:
x^2 + 16 = 25
Subtracting 16 from both sides, we get:
x^2 = 9
Taking the square root of both sides, we find:
x = 3 or -3
Since distance cannot be negative, the base of the ladder should be placed 3 meters away from the building.