A walking path is shaped like a rectangle with a width 7 times its length l. what is a simplified expression for the distance between opposite corners of the walking path?

The simplified expression is d = (5√2) L

Step-by-step explanation:

* Lets explain the problem

- A walking path is shaped like a rectangle

- The width of the rectangle is 7 times its length L

∵ The length of the rectangle is L

∵ The width is 7 times the length

∴ The width of the rectangle is 7L

- The distance between the opposite corners represented by the

diagonal of the rectangle

- The length, the width and the diagonal formed a right triangle

- Its hypotenuse is the diagonal of the rectangle

- Its two legs are the length and the width of the rectangle

* Now we have right triangle use the Pythagoras Theorem to find

the hypotenuse

∵ The length, the width and the diagonal of the rectangle are the

sides of a right triangle

∵ The diagonal is the hypotenuse (h) of the triangle

∵ hypotenuse = √[L² + W²]

∵ The length = L and the width = 7L

∴ h = √[ (L) ² + (7L) ²] = √[L² + 49L²] = √[50L²]

∵ √50 = 5√2

∵ √ (L²) = L

∴ h = 5√2 L

∵ The diagonal of the rectangle is the distance between the

opposite corners

∴ The distance between the opposite corners is (5√2) L

* The simplified expression is d = (5√2) L, where L is the length

of the rectangle