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Question

a rectangular garden measures 30 feet 8 inches wide and 40 feet 6 inches long. a diagonal path cuts across the garden. if shariff walks down the diagonal and once around the garden, how far will she walk?

Answer 1

First, let's change those measures into numbers that are easier to work with. 8 inches is 8/12 = 2/3 feet, and 6 inches is 6/12 = 1/2 feet. So, the garden is 30 2/3 feet wide and 40 1/2 feet long.

 

To find the length of the diagonal, you'll need to treat this as a right triangle with legs 30 ²/₃ and 40 ¹/₂ and hypotenuse x. Then you can use the Pythagorean Theorem (a² + b² = c²) to solve for the hypotenuse:

 

(30 ²/₃)² + (40 ¹/₂)² = x²

940 ⁴/₉ + 1640 ¹/₄ = x²

940 ¹⁶/₃₆ + 1640 ⁹/₃₆ = x²

2580 ²⁵/₃₆ = x²

x = 50.8 feet (approximately)

 

So, if Shariff walks around the whole garden and down the diagonal, she walks the width twice, the length twice, and the diagonal once. In other words:

 

2(30 ²/_³) + 2(40 ¹/₂) + (50.8) = 61 ¹/₃ + 81 + 50.8 = 193.13 feet (approximately)