Jill can walk to his school along the road beside a rectangular field or he can cut diagonally across the field.( Corner to corner). The field is 170 m by 90 m.1) Calculate the diagonal distance across the field.2) How much distance does Jill save by taking this shortcut across the field?Round your answer to 1 decimal place and put only the number in the box with no units.)
Question
Jill can walk to his school along the road beside a rectangular field or he can cut diagonally across the field.( Corner to corner). The field is 170 m by 90 m.1) Calculate the diagonal distance across the field.2) How much distance does Jill save by taking this shortcut across the field?Round your answer to 1 decimal place and put only the number in the box with no units.)
Solution
- To calculate the diagonal distance across the field, we can use the Pythagorean theorem, which states that in a right-angled 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 lengths of the other two sides. In this case, the sides of the rectangle are the two sides of the triangle, and the diagonal is the hypotenuse.
So, the length of the diagonal (d) can be calculated as follows:
d = sqrt((170^2) + (90^2))
d = sqrt((28900) + (8100))
d = sqrt(37000)
d = 192.5 m (rounded to 1 decimal place)
- The distance Jill would walk if he followed the road is the sum of the two sides of the field, which is 170 m + 90 m = 260 m.
So, the distance Jill saves by taking the shortcut across the field is the difference between the distance along the road and the diagonal distance:
Distance saved = 260 m - 192.5 m = 67.5 m (rounded to 1 decimal place)
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