A disoriented driver crosses diagonally from one corner of a 150 m by 275 m lawn to the far corner. How far does the wayward driver drive across the lawn? Give an approximate answer to three decimal places.
What formula would I apply to solve this?
Responses
Math word problem - drwls, Monday, October 27, 2008 at 6:19am
A diagonal line between opposite corners of a rectangle (the lawn) forms two right triangles. Apply the Pythagorean theorem to either of those triangles. The diagonal will be the hypotenuse in the formula.
is the answer 308.750 m or did I do something wrong?
sqrt[(150)^2 + (275)^2] does not equal 308.75..
It is 313.249 (rounded off to three decimal places, as they requested)
oh okay, I see what I did wrong sorry.
Thank you
To solve this problem, you would apply the Pythagorean theorem. This theorem states that in a right 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 other two sides.
In this case, the lawn forms a rectangle with sides of 150 m and 275 m. The diagonal the driver travels is the hypotenuse of a right triangle within this rectangle.
To find the length of the diagonal, you can use the Pythagorean theorem:
Diagonal^2 = length^2 + width^2
Diagonal^2 = 150^2 + 275^2
Diagonal^2 = 22500 + 75625
Diagonal^2 = 98125
Taking the square root of both sides, you get:
Diagonal = sqrt(98125)
Using a calculator, the approximate value of the diagonal is:
Diagonal ≈ 313.098 m
So the approximate distance the wayward driver drives across the lawn is 313.098 meters.