Please Helpppp!!! Mother having a hard time with radicals.
A playground is shaped like a rectangle with a width 5 times its length (l). What is a simplified expression for the distance between opposite corners of the playground? Please can you post step-by-step so I understand what I am grading
length --- l
width ---- 5l
distance^2 = (5l)^2 + l^2 = 26l^2
distance = √26 l
Thanks Reiny, I appreciate the steps. :)
To find the distance between opposite corners of the playground, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length of the rectangle can be represented by "l," and the width is given as 5 times the length, so the width can be represented as "5l."
Let's assume the length of the playground is "l," and the width is "5l." We can draw a right triangle ABC, where AB represents the length of the playground (l), BC represents the width (5l), and AC represents the distance between opposite corners.
Now, we can apply the Pythagorean theorem:
AC^2 = AB^2 + BC^2
Substituting the given values:
AC^2 = l^2 + (5l)^2
Simplifying:
AC^2 = l^2 + 25l^2
AC^2 = 26l^2
To find the simplified expression for the distance between opposite corners, we take the square root of both sides:
AC = √(26l^2)
We can simplify this expression further by factoring out the square root of 26:
AC = √(26)√(l^2)
AC = √(26) * l
Therefore, the simplified expression for the distance between opposite corners of the playground is √(26) * l.