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MATH / In triangle ABC, AB=√(30), AC=√(6), and BC=√(15). There is a point D for which (AD)¯ bisects (BC)¯, and ∠ADB is a right angle. Find the value of the ratio ([ADB])/([ABC]).In other …

Problem

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problem

In triangle ABCABC, AB=30AB=\sqrt{30}, AC=6AC=\sqrt{6}, and BC=15BC=\sqrt{15}. There is a point DD for which AD¯\overline{AD} bisects BC¯\overline{BC}, and ∠ADB\angle ADB is a right angle. Find the value of the ratio [ADB][ABC].\dfrac{[ADB]}{[ABC]}.In other words, compute the ratio of the area of triangle ADBADB to the area of triangle ABC.ABC.
Plain-text mathematical notation (without MathML)
In triangle ABC, AB=√(30), AC=√(6), and BC=√(15). There is a point D for which (AD)¯ bisects (BC)¯, and ∠ADB is a right angle. Find the value of the ratio
([ADB])/([ABC]).In other words, compute the ratio of the area of triangle ADB to the area of triangle ABC.
Original LaTeX notation
In triangle $ABC$, $AB=\sqrt{30}$, $AC=\sqrt{6}$, and $BC=\sqrt{15}$. There is a point $D$ for which $\overline{AD}$ bisects $\overline{BC}$, and $\angle ADB$ is a right angle. Find the value of the ratio
\[\dfrac{[ADB]}{[ABC]}.\]In other words, compute the ratio of the area of triangle $ADB$ to the area of triangle $ABC.$

level

Level 4

type

Precalculus

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Source and history

task_id
7dffa1de-3a9d-54fc-9c68-1c36ae3f6824
task_key
precalculus--test--7dffa1de-3a9d-54fc-9c68-1c36ae3f6824
task_revision_id
1
config / split
precalculus / test

Official source

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