(1) Someone uses one side (the wall is 7.5 meters long) and a 13 meter long bamboo fence as the other three sides to form a rectangular vegetable garden with an area of 20 square meters How many meters are the length and width of the square garden? (2) if the area in (1) is 23 square meters, can it be enclosed into a rectangular garden that meets the conditions? Why?

(1) Someone uses one side (the wall is 7.5 meters long) and a 13 meter long bamboo fence as the other three sides to form a rectangular vegetable garden with an area of 20 square meters How many meters are the length and width of the square garden? (2) if the area in (1) is 23 square meters, can it be enclosed into a rectangular garden that meets the conditions? Why?

Let the side perpendicular to the wall (that is, the width) be x meters in length. The solution of the equation x (13-2x) = 20 is x 1 = 4, x 2 = 2.5. Test 13-2 × 2.5 = 8 ＞ 7.5, so x 2 is rounded off so that the length is 5 meters and the width is 4 meters. The second problem x (13-2x) = 20 has no real root, so it can't be adopted by pure hand

To use a 13 meter long fence, one side against the wall, surrounded by an area of 20 square meters of rectangular field, then its length and width

Let x = - 13
X(13-X)/2=20
X²-13X+40=0
（X-5)(X-8)=0
X1=5 X2=8
When length = 5m, width = 8 / 2 = 4m
When length = 8m, width = 5 / 2 = 2,5m