Year 10 Maths Find the length and width that will maximize the area of rectangle

liang123993

New member

The question is in the image. Working out with every step would be much appreciated.

Greg

Perseverance
Staff member
Here's a start:

Let $W$ be width, $L$ be length an $A$ be the desired area. Then,

$$\displaystyle 5W+2L=550$$

$$\displaystyle LW=A$$

Can you make any progress from there?

Greg

Perseverance
Staff member
Here's a start:

Let $W$ be width, $L$ be length an $A$ be the desired area. Then,

$$\displaystyle 5W+2L=550$$

$$\displaystyle LW=A$$

Can you make any progress from there?
$$\displaystyle W=\frac AL$$

$$\displaystyle \frac{5A}{L}+2L=550$$

$$\displaystyle 5A+2L^2=550L$$

$$\displaystyle A=110L-\frac{2L^2}{5}$$

$A$ has a maximum at the vertex of this inverted parabola, so $L=\frac{275}{2}$. Finding $A$ and $W$ from here should be straightforward.