Patricia's teacher asked her to find the perimeter of the school's rectangular parking lot. After school, patricia walks along the short side of the lot and finds it is 50 yards long. She then walks diagonally from one corner of the rectangle to the other and throught the exit to go home. She finds that the distance of the diagonal is 130 yards. Patricia decides that this is enough information to determine the perimeter of the track. Based on her information, what is the perimeter of the parking lot?
so I did 50^2 + b^2 = 130^2
2500+b^2=16,900
b^2=14,400
b=120
so the choices are:
a. 100 yards
b. 110 yards
c. 120 yards
d. 180 yards
But I get for the perimeter
50+50+120+120=340
what am I doing wrong?
If the question is as you typed it, there is nothing that you did wrong.
I recognized your dimensions as multiples of 10 of the basic 5,12, 13 right-angled triangle.
It wouldn't be the first time that a textbook has wrong answers.
To find the perimeter of a rectangle, you need to add up the lengths of all four sides. However, it seems like you calculated the length of only two sides (both short sides) of the parking lot.
Let's label the sides of the rectangle:
Short side: 50 yards
Long side: b yards
From Patricia's measurements, she walked along one short side and the diagonal, which is equivalent to one long side.
Using the Pythagorean theorem, we have:
50^2 + b^2 = 130^2
2500 + b^2 = 16900
b^2 = 14400
b = 120
Now that we know the length of the long side is 120 yards, we can find the perimeter by adding up all four sides:
Perimeter = 2 * (Short side + Long side)
Perimeter = 2 * (50 + 120)
Perimeter = 2 * 170
Perimeter = 340 yards
Therefore, the correct answer for the perimeter of the parking lot is 340 yards, as you calculated.