As shown in the figure, in the square ABCD, e is the midpoint of AB side, G and F are the points on AD and BC side respectively. If Ag = 1, BF = 2, ∠ GEF = 90 °, then the length of GF is______ ．

As shown in the figure, in the square ABCD, e is the midpoint of AB side, G and F are the points on AD and BC side respectively. If Ag = 1, BF = 2, ∠ GEF = 90 °, then the length of GF is______ ．

The quadrilateral ABCD is a square, the square, the square, the square, the square, the square, the square, the \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ of So the answer is: 3

Make a rectangle inside an isosceles right triangle and cut it on the two adjacent sides of the rectangle. If the waist length of the isosceles triangle is 10cm
Then the maximum area of rectangle ABCD is?

25 square centimeters
It's just a square

As shown in the figure, in the isosceles trapezoid ABCD, ab ∥ DC, ∠ DAB = 45 °, ab = 10cm, CD = 4cm. The hypotenuse Mn of isosceles right triangle PMN is 10cm, point a coincides with point n, and Mn and ab are in a straight line. If the isosceles trapezoid ABCD does not move, the isosceles right triangle PMN moves to the right at the speed of 1cm / s along the line where AB is located until point n coincides with point B
(1) The shape of the overlapping part of isosceles right triangle PMN and isosceles trapezoid ABCD is determined by______ The shape changes to______ (2) when the isosceles right triangle PMN moves x (s), the overlapping area of isosceles right triangle PMN and isosceles trapezoid ABCD is y (cm2), and the functional relationship between Y and X is obtained; (3) when ① x = 4 (s), ② x = 8 (s), the overlapping area of isosceles right triangle PMN and isosceles trapezoid ABCD is obtained

(1) The isosceles right angles △ PMN, ∠ DAB = 45 °, ∠ PNM = ∠ DAB = 45 °,  AEN = 180 ° - 45 ° - 45 ° = 90 ° are isosceles right triangles, as shown in Figure 2. The shape of the overlapping part is isosceles when 0 ＜ x ≤ 6 Right triangle ean (as shown in Figure 1), where an = x (CM), passing point E as eh ⊥ AB at point h, then eh bisects an, ∧ eh = 12An = 12x, ∧ y = s △ ane = 12An · eh = 12x · 12x = 14x2, ② when 6 ＜ x ≤ 10, the shape of the overlapping part is isosceles trapezoid aned (as shown in Figure 2), at this time, an = x (CM), CE = BN = 10-x, de = 4 - (10-x) = X-6, passing point D as DF ⊥ AB at F, passing point C as CG ⊥ AB can be obtained For G, then AF = BG, DF = AF = 12 (10-4) = 3, ｜ y = s trapezoid, aned = 12 (de + an) · DF = 12 (X-6 + x) × 3 = 3x-9. Answer: the functional relation between Y and X is y = 14x2 (0 < x ≤ 6) or (3) ① when x = 4 (s), y = 14x2 = 14 × 42 = 4; ② when x = 8 (s), y = 3x-9 = 3 × 8-9 = 15. Answer: ① when x = 4 (s), the overlapping area of isosceles right triangle PMN and isosceles trapezoid ABCD is 4cm2; ② when x = 8 (s), the overlapping area of isosceles right triangle PMN and isosceles trapezoid ABCD is 15cm2