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MATH / Triangle ABC is isosceles, with AB=AC and altitude AM=11. Suppose that there is a point D on (AM)¯ with AD=10 and ∠BDC=3∠BAC. Find the perimeter of triangle ABC. [asy] unitsize(0.4…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Triangle ABCABC is isosceles, with AB=ACAB=AC and altitude AM=11.AM=11. Suppose that there is a point DD on AM¯\overline{AM} with AD=10AD=10 and ∠BDC=3∠BAC.\angle BDC=3\angle BAC. Find the perimeter of triangle ABC.ABC. [asy] unitsize(0.4 cm); pair A, B, C, D, M; A = (0,11); D = (0,1); B = (-11/2,0); C = (11/2,0); M = (B + C)/2; draw(A--B--C--cycle); draw(A--M); draw(B--D--C); label("AA", A, N); label("BB", B, SW); label("CC", C, SE); label("DD", D, NW); label("MM", M, S); [/asy]
Plain-text mathematical notation (without MathML)
Triangle ABC is isosceles, with AB=AC and altitude AM=11. Suppose that there is a point D on (AM)¯ with AD=10 and ∠BDC=3∠BAC.  Find the perimeter of triangle ABC.

[asy]
unitsize(0.4 cm);

pair A, B, C, D, M;

A = (0,11);
D = (0,1);
B = (-11/2,0);
C = (11/2,0);
M = (B + C)/2;

draw(A--B--C--cycle);
draw(A--M);
draw(B--D--C);

label("A", A, N);
label("B", B, SW);
label("C", C, SE);
label("D", D, NW);
label("M", M, S);
[/asy]
Original LaTeX notation
Triangle $ABC$ is isosceles, with $AB=AC$ and altitude $AM=11.$ Suppose that there is a point $D$ on $\overline{AM}$ with $AD=10$ and $\angle BDC=3\angle BAC.$  Find the perimeter of triangle $ABC.$

[asy]
unitsize(0.4 cm);

pair A, B, C, D, M;

A = (0,11);
D = (0,1);
B = (-11/2,0);
C = (11/2,0);
M = (B + C)/2;

draw(A--B--C--cycle);
draw(A--M);
draw(B--D--C);

label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$D$", D, NW);
label("$M$", M, S);
[/asy]

level

Level 4

type

Precalculus

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Source and history

task_id
9443d867-1f9e-5a1b-ae21-172427252308
task_key
precalculus--test--9443d867-1f9e-5a1b-ae21-172427252308
task_revision_id
1
config / split
precalculus / test

Official source

initial import