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

or

one leg was 129.29 , then the other leg was 270.71

check

270.71^2 + 129.29^2 = 89999.8 or appr 90000 = 300^2

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