There are four digits ABCD, and ABCD = (AB + CD) square, find all such four digits

There are four digits ABCD, and ABCD = (AB + CD) square, find all such four digits

2025 3025 9801

It is known that in rectangular trapezoid ABCD, ad ∥ BC, ab ⊥ BC, ad = 2, BC = DC = 5, and point P moves on BC, then when PA + PD takes the minimum value, the height of edge AP in △ APD is ()
A. 21717B. 41717C. 81717D. 3

Through point D, make de ⊥ BC in E, ≁ ad ∥ BC, ab ⊥ BC, ≁ quadrilateral abed is rectangular, ≁ be = ad = 2, ≁ BC = CD = 5, ≁ EC = 3, ≁ AB = de = 4, extend AB to a ′, make a ′ B = ab, connect a ′ d with BC in P, then PA + PD is minimum, that is, when p is on the middle perpendicular of AD, PA + PD takes the minimum, and≁ B is AA ′

In right angle trapezoid ABCD, AD / / BC, ∠ B = 90 °, ad = 2, BC = 4, point P slides on the edge of AB, if △ DAP is similar to △ PBC, and AP = 3, calculate BP

Delta DAP is similar to delta PBC in two ways
1,△APD∽△BPC
In this case, AP: Pb = ad: BC, let Pb = x, then AP = 9-x
∴(9-X):X=2:4
We get x = 6, that is Pb = 6
2,△APD∽△BCP
If AP: BC = ad: BP, Pb = x, then AP = 9-x
There are: (9-x): 4 = 2: X
We get X1 = 1, X2 = 8
So Pb = 1, or Pb = 8