SOLUTION: "A rectangular plot of ground measures 48 meters by 20 meters. The owner plans to put a diagonal walk from one corner to the opposite corner. How long will the walk be?" This ques

Algebra ->  Rectangles -> SOLUTION: "A rectangular plot of ground measures 48 meters by 20 meters. The owner plans to put a diagonal walk from one corner to the opposite corner. How long will the walk be?" This ques      Log On


   

Question 537198: "A rectangular plot of ground measures 48 meters by 20 meters. The owner plans to put a diagonal walk from one corner to the opposite corner. How long will the walk be?"
This question is confusing me because I don't understand how to find the middle!
Found 2 solutions by rfer, lmeeks54:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
a^2+b^2=c^2
48^2+20^2=c^2
2304+400=2704
c= sqrt 2704
c=52 meters

Answer by lmeeks54(111) About Me  (Show Source):
You can put this solution on YOUR website!
You don't have to find the middle. The problem is a tricky way to get you to think about right triangles. A rectangle has 4 equal angles of 90 degrees each and normally two equal length long sides and two equal length short sides. If you slice that rectangle from corner to corner with a diagonal line, you end up with two right triangles facing each other.
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The Pythagorean Theorem states that for a right triangle, the formula linking the lengths of the sides is given by:
c^2 = a^2 + b^2 where c = the hypotenuse (the diagonal walk for your problem) and a and b are the short and long sides of the rectangle (also called the base and height of the right triangle).
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You are given:
a = 48 meters
b = 20 meters
we just need to solve for c now:
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c^2 = a^2 + b^2 can be simplified by taking the sqrt of both sides:
c = sqrt(a^2 + b^2)
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Just substitute in the values for a and b given above and solve for c:
c = sqrt(48^2 + 20^2)
c = sqrt(2304 + 400)
c = 52 meters is the length of your diagonal sidewalk...
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cheers,
Lee