Draw the largest square in a right triangle. The known bottom is 10cm and the height is 30cm. Find the side length of the square Draw the largest square in a right triangle. The known bottom is 10cm and the height is 30cm. Find the side length of the square,

Draw the largest square in a right triangle. The known bottom is 10cm and the height is 30cm. Find the side length of the square Draw the largest square in a right triangle. The known bottom is 10cm and the height is 30cm. Find the side length of the square,

Let the side length of a square be X
x∶10＝（30－x）∶30
30x＝10×（30－x）
30x＝300－10x
40x＝300
x＝7.5

As shown in the figure, in △ ABC, ab = AC, D is the point on BC, connecting ad, point E is on ad, passing through point E is em ⊥ AB, en ⊥ AC, and the perpendicular feet are points m and N respectively
(1) if ad, BC, is em equal to en? Please explain the reason
(2) if EM = em, is ad perpendicular to BC? Please explain the reason

What conclusion can be conjectured by proving EM = en: ∵ AB = AC, ad ⊥ BC ∧ Mae = the conclusion obtained by proving is: any point on the high line at the bottom of isosceles triangle, to the point at the two waists

In trapezoidal ABCD, AD / / BC, am = DM, BN = CN, and angle B + angle c = 90 degrees. If ad = 12cm, BC = 20cm, find the length of Mn

Extend Ba, CD to point E, connect en, ad to point F
Because angle B + angle c = 90 degrees
So the angle e = 90 degrees
Because BN = CN
So angle c = angle Cen
Because AD / / BC
So angle ade = angle c
So angle ade = angle Cen
Because the angle e = 90 degrees
So angle ead = angle AEF
So AF = FD = EF
Because am = DM
So point F is point M
Because the angle e = 90 degrees, BN = CN
So en = 1 / 2BC
Because angle e = 90 degrees, am = DM
So EM = 1 / 2ad
So Mn = en-em = 1 / 2 (BC-AD)
Because BC = 20cm, ad = 12cm
So Mn = 4cm