Question

A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have seen area of 425 feet squared. How wide will the sidewalk be?

Answer 1

So the original lawn has an area
24 × 32 = 768 the new lawn will have area 425
this means the area of the sidewalk will be 768-425=343
now the sidewalk is a certain width of we draw it out and label it x we see the lawn has an area of
$(32 - 2x)(24 - 2x) = 425 \\ 768 - 64x - 48x + 4 {x}^{2} = 425 \\ 4 {x}^{2} - 112x + 343 = 0$
use the quadratic formula to solve. then you will know how wide the sidewalk is. I will attach picture