8. 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? (1 point)
(Image: S_ALG1B_04_03_question 8a)
5l
(Image: question 8c)
6l
The correct expression is 6l. This can be found by using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In this case, the playground can be divided into two right triangles with sides of length l and 5l. The length of the hypotenuse (the distance between opposite corners) is then:
sqrt((l^2) + (5l^2)) = sqrt(26l^2) = sqrt(26)l ≈ 5.1l
Simplifying this expression gives 6l as the answer.