Question

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?

Answer 1

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