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imc

geometry intermediate

Problem

In rectangle

A B C D

,

A D = 1

,

P

is on

\overline{A B}

, and

\overline{D B}

and

\overline{D P}

trisect

∠ A D C

. What is the perimeter of

△ B D P

?

problem

(A)

3 + \frac{3}{3}

(B)

2 + \frac{4 3}{3}

(C)

2 + 22

(D)

\frac{3 + 3 5}{2}

Solution

A D = 1

. Since

∠ A D C

is trisected,

∠ A D P = ∠ P D B = ∠ B D C = 3 0^{\circ}

. Thus,

P D = \frac{2 3}{3}

D B = 2

B P = 3 - \frac{3}{3} = \frac{2 3}{3}

. Adding, we get

2 + \frac{4 3}{3}

.

Final answer

B