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