35 decimeter string is attached to both ends of a 25 decimeter pole. At what point of the string do you need to pull to make a right triangle?
lets see..sum of one leg and hypotensues is 35
25^2+L^2=H^2
but 35=L+H or H=35-L
625=(35-L)^2-L^2
solve for L
Hmm that's what I also thought when I tried to solve this. I get 70L = 600 so L = 600/70 therefore L ~ 8.57
Answer given is 20 dm (or 15 dm) depending on which end of the pole I suppose.
To find the point on the string where you need to pull to make a right triangle, we need to first understand the concept of a right triangle.
A right triangle is a type of triangle that has one angle measuring 90 degrees (a right angle). In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.
In this case, we have a pole with a length of 25 decimeters and a string attached to both ends of the pole, each with a length of 35 decimeters.
To create a right triangle, we need to pull the string at a point that is equidistant from both ends of the pole. This point will be exactly at the midpoint of the string.
To find the midpoint of the string, we can use the formula:
Midpoint = (Length of one end of the string + Length of the other end of the string) / 2.
In this case, the length of one end of the string is 35 decimeters, and the length of the other end is also 35 decimeters:
Midpoint = (35 decimeters + 35 decimeters) / 2
= 70 decimeters / 2
= 35 decimeters.
So, to create a right triangle, you need to pull the string at the midpoint, which is 35 decimeters from either end of the string.
By pulling at this point, you will ensure that the two legs of the triangle are equal in length, and the hypotenuse formed by the pole and the pulled string will be perpendicular to the legs, forming a right angle.