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MATH / In any isosceles triangle ABC with AB=AC, the altitude AD bisects the base BC so that BD=DC. As shown in △ABC, AB=AC=25 and BC=14. Determine the length of the altitude AD. [asy] dr…

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

problem

In any isosceles triangle ABCABC with AB=ACAB=AC, the altitude ADAD bisects the base BCBC so that BD=DCBD=DC. As shown in △ABC\triangle ABC, AB=AC=25AB=AC=25 and BC=14BC=14. Determine the length of the altitude ADAD. [asy] draw((0,0)--(14,0)--(7,24)--cycle,black+linewidth(1)); draw((7,24)--(7,0),black+linewidth(1)+dashed); draw((7,0)--(7,1)--(6,1)--(6,0)--cycle,black+linewidth(1)); draw((5.5,-4)--(0,-4),black+linewidth(1)); draw((5.5,-4)--(0,-4),EndArrow); draw((8.5,-4)--(14,-4),black+linewidth(1)); draw((8.5,-4)--(14,-4),EndArrow); label("AA",(7,24),N); label("BB",(0,0),SW); label("CC",(14,0),SE); label("DD",(7,0),S); label("25",(0,0)--(7,24),NW); label("25",(7,24)--(14,0),NE); label("14",(7,-4)); [/asy]
Plain-text mathematical notation (without MathML)
In any isosceles triangle ABC with AB=AC, the altitude AD bisects the base BC so that BD=DC.

As shown in △ABC, AB=AC=25 and BC=14.  Determine the length of the altitude AD.

[asy]
draw((0,0)--(14,0)--(7,24)--cycle,black+linewidth(1));
draw((7,24)--(7,0),black+linewidth(1)+dashed);
draw((7,0)--(7,1)--(6,1)--(6,0)--cycle,black+linewidth(1));
draw((5.5,-4)--(0,-4),black+linewidth(1));
draw((5.5,-4)--(0,-4),EndArrow);
draw((8.5,-4)--(14,-4),black+linewidth(1));
draw((8.5,-4)--(14,-4),EndArrow);
label("A",(7,24),N);
label("B",(0,0),SW);
label("C",(14,0),SE);
label("D",(7,0),S);
label("25",(0,0)--(7,24),NW);
label("25",(7,24)--(14,0),NE);
label("14",(7,-4));
[/asy]
Original LaTeX notation
In any isosceles triangle $ABC$ with $AB=AC$, the altitude $AD$ bisects the base $BC$ so that $BD=DC$.

As shown in $\triangle ABC$, $AB=AC=25$ and $BC=14$.  Determine the length of the altitude $AD$.

[asy]
draw((0,0)--(14,0)--(7,24)--cycle,black+linewidth(1));
draw((7,24)--(7,0),black+linewidth(1)+dashed);
draw((7,0)--(7,1)--(6,1)--(6,0)--cycle,black+linewidth(1));
draw((5.5,-4)--(0,-4),black+linewidth(1));
draw((5.5,-4)--(0,-4),EndArrow);
draw((8.5,-4)--(14,-4),black+linewidth(1));
draw((8.5,-4)--(14,-4),EndArrow);
label("$A$",(7,24),N);
label("$B$",(0,0),SW);
label("$C$",(14,0),SE);
label("$D$",(7,0),S);
label("25",(0,0)--(7,24),NW);
label("25",(7,24)--(14,0),NE);
label("14",(7,-4));
[/asy]

level

Level 3

type

Prealgebra

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Source and history

task_id
98cead55-2ad9-529c-b9b4-33d7dc37f5b8
task_key
prealgebra--test--98cead55-2ad9-529c-b9b4-33d7dc37f5b8
task_revision_id
1
config / split
prealgebra / test

Official source

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