As shown in the figure, the rectangle efgh is connected to △ ABC, the bottom edge of △ ABC AC = B, the height BD = h, and the height eh = X. try to write out the functional relationship between the rectangle area s and X, and find out the value range of X

∵ rectangle efgh is connected to △ ABC, the bottom edge of △ ABC is AC = B, high BD = h, the height of rectangle is eh = x, ∵ eh = MD = x, BM = h-x, and △ BHG ∵ BAC, ∵ hgac = bmbd, that is HGB = h-xh, GH = B (h-x) h, so s = x · B (h-x) H = - bhx2 + BX (0 < x < h)

As shown in the figure, the quadrilateral efgh is △ ABC inscribed square, BC = 27cm, height ad = 21cm, calculate the area of the inscribed square efgh

Let the side length of square efgh be x, let the intersection of AD and GH be I, ∵ Hg ∥ BC, ∥ AHG ∥ ABC, ∥ AI: ad = GH: BC, the side length of square efgh be xcm. ∵ BC = 27, ad = 21, ∥ (21-x): 21 = X: 27, the solution is: x = 18916, ∥ the area of inscribed square efgh is (18916) 2 = 35721256cm2

As shown in the figure, the quadrilateral efgh is △ ABC inscribed square, BC = 21cm, height ad = 15cm, then the side length EF of the inscribed square=______ ．

Let the side length of a square be equal to x, efgh be a square, GH BC, AGH ACB, AgI ACD, ghbc = agac, agac = aiad, ghbc = aiad, X21 = 15 − x15, x = 8.75, that is, EF = 8.75cm

As shown in the figure, the quadrilateral efgh is △ ABC inscribed square, BC = 27cm, height ad = 21cm, calculate the area of the inscribed square efgh

It is known that efgh is a triangle ABC inscribed square, BC = 31cm, ad is the height of the triangle ABC and ad = 15cm?

Let the side length be x / 31 = 15-x / 15 (the ratio of height corresponding to similar triangles is equal to the recognition ratio) x = 465 / 46

In the RT triangle ABC, the angle ABC = 90 degrees, CD is the height of the edge AB, the perimeter of the triangle ABC is 60, BC: AC = 5:12, find the length of AB and CD

The problem is wrong, should be angle ACB = 90 degrees
Let BC = 5x, then AC = 12x, AB ^ 2 = √ (AC ^ 2 + BC ^ 2) = 13X
5X+12X+13X=60
X=2
AB=13X=26,BC=5X=10,AC=12X=24
CD=BC*AC/AB=120/13

How to cut the largest square in an acute triangle
It's better to be a little short~

Using similarity
The ratio of the bottom is equal to the ratio of the high

The relationship between the area of an acute triangle and its inscribed square

If there is a square in a triangle, the square is half the area of the triangle,
The height and bottom of a triangle

Let the length of the square side a, the height of the triangle h, and the bottom B, then
bh/2=2a^2
a/b=(h-a)/h
So a = H / 2, B = H
That is, when B = h, the square is half the area of the triangle

If there is a square in an acute triangle whose vertices are all on the edge of the triangle, the relationship between the area of the square and the area of the original triangle?

Let the length of the triangle be a, B, C, and the height of the two points on the side be H. the length of the two points on the side of C is D. the area of the triangle = D * D + 1 / 2 (C-D) * D + 1 / 2 (H-D) * D = 1 / 2hc, so CD + HD = HC, H = CD / (C-D), so the area of the triangle = 1 / 2hc = 1 / 2C ^ 2D / (C-D), and the area of the square is 2 times that of the original triangle = C ^ 2 / {4D (C-D)}

As shown in the figure, the rectangle efgh is connected to △ ABC, the bottom edge of △ ABC AC = B, the height BD = h, and the height eh = X. try to write out the functional relationship between the rectangle area s and X, and find out the value range of X