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Omni-MATH / The quadrilateral ABCD has the following equality ∠ABC=∠BCD=150^(∘). Moreover, AB=18 and BC=24, the equilateral triangles △APB,△BQC,△CRD are drawn outside the quadrilateral. If …

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problem

The quadrilateral ABCDABCD has the following equality ∠ABC=∠BCD=150∘\angle ABC=\angle BCD=150^{\circ}. Moreover, AB=18AB=18 and BC=24BC=24, the equilateral triangles △APB,△BQC,△CRD\triangle APB,\triangle BQC,\triangle CRD are drawn outside the quadrilateral. If P(X)P(X) is the perimeter of the polygon XX, then the following equality is true P(APQRD)=P(ABCD)+32P(APQRD)=P(ABCD)+32. Determine the length of the side CDCD.
Plain-text mathematical notation (without MathML)
The quadrilateral ABCD has the following equality ∠ABC=∠BCD=150^(∘). Moreover, AB=18 and BC=24, the equilateral triangles △APB,△BQC,△CRD are drawn outside the quadrilateral. If P(X) is the perimeter of the polygon X, then the following equality is true P(APQRD)=P(ABCD)+32. Determine the length of the side CD.
Original LaTeX notation
The quadrilateral $ABCD$ has the following equality $\angle ABC=\angle BCD=150^{\circ}$. Moreover, $AB=18$ and $BC=24$, the equilateral triangles $\triangle APB,\triangle BQC,\triangle CRD$ are drawn outside the quadrilateral. If $P(X)$ is the perimeter of the polygon $X$, then the following equality is true $P(APQRD)=P(ABCD)+32$. Determine the length of the side $CD$.

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task_id
ea755906-4842-5f81-be86-181491ebc58f
task_key
test--ea755906-4842-5f81-be86-181491ebc58f
task_revision_id
1
config / split
/ test

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