Posted by danielle on Thursday, April 25, 2013 at 12:39am.
On the sidewalk the distance from the dormitory to the cafeteria is 400 meters. By cutting across the lawn, the walking distance is shortened to 300 meters. how long is each part of the L shaped sidewalk?
math hw (algebra) - Reiny, Thursday, April 25, 2013 at 9:29am
I visualize a right angled triangle with sides
y, 400-y, and hypotenuse 300
There will be large numbers , so here is a little trick
let x be multiples of 100
so we have
x, 4-x, and 3 as the sides of a right-angled triangle
x^2 + (4-x)^2 = 3^2
x^2 + 16 - 8x + x^2 = 9
2x^2 - 8x + 7 = 0
x = (8 ± √8)/4
= 2.7071 or 1.2929
but x was a multiple of 100
so one leg was 270.71 , the other 400-270.71 or 129.29 m
one leg was 129.29 , then the other leg was 270.71
270.71^2 + 129.29^2 = 89999.8 or appr 90000 = 300^2
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