tmua 2023 Q5

tmua · Uk · paper1 1 marks Stationary points and optimisation Geometric or applied optimisation problem

The following shape has two lines of reflectional symmetry.
$M N O P$ is a square of perimeter 40 cm .
The vertices of rectangle $R S T U$ lie on the edge of square $M N O P$.
$M R$ has length $x \mathrm {~cm}$.
What is the largest possible value of $x$ such that $R S T U$ has area $20 \mathrm {~cm} ^ { 2 }$ ?

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The following shape has two lines of reflectional symmetry.

$M N O P$ is a square of perimeter 40 cm .

The vertices of rectangle $R S T U$ lie on the edge of square $M N O P$.

$M R$ has length $x \mathrm {~cm}$.

What is the largest possible value of $x$ such that $R S T U$ has area $20 \mathrm {~cm} ^ { 2 }$ ?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20