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OlympiadBench / 2254 / Square OPQR has vertices O(0,0),P(0,8),Q(8,8), and R(8,0). The…

Problem

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

question

Square

O P Q R

has vertices

O(0,0), P(0,8), Q(8,8)

, and

R(8,0)

. The parabola with equation

y=a(x-2)(x-6)

intersects the sides of the square

O P Q R

at points

K, L, M

, and

N

. Determine all the values of

a

for which the area of the trapezoid

K L M N

is 36 .

Plain-text mathematical notation (without MathML)

Square OPQR has vertices O(0,0),P(0,8),Q(8,8), and R(8,0). The parabola with equation y=a(x−2)(x−6) intersects the sides of the square OPQR at points K,L,M, and N. Determine all the values of a for which the area of the trapezoid KLMN is 36 .

Original LaTeX notation

Square $O P Q R$ has vertices $O(0,0), P(0,8), Q(8,8)$, and $R(8,0)$. The parabola with equation $y=a(x-2)(x-6)$ intersects the sides of the square $O P Q R$ at points $K, L, M$, and $N$. Determine all the values of $a$ for which the area of the trapezoid $K L M N$ is 36 .

answer type

Numerical

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2254
task_id: ef9d4299-fdbf-540a-9532-a867b1257209
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2254
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import