Question

known amount of length and width of a rectangle is 15 cm. What is the maximum area of the rectangle?

Answer 1

// p = rectangle length

l = rectangle width

L = rectangular area //

p + l = 15cm

p = 15cm - l

L rectangle = pl

= (15cm-l) (l)

= 15cm l - l²

// then the maximum area is when p and l are equal //

p = l

// finds l by substituting p //

p + l = 15cm

l + l = 15cm

2l = 15cm

l = 15cm / 2

l = 7,5cm

p = l

= 7.5cm

// find the maximum area of the rectangle by substituting l //

L rectangle = 15cm l - l²

= 15cm (7.5cm) - (7.5cm )²

= 112.5cm² - 56.25cm²

= 56.25cm²

So the maximum area of the rectangle is 56.25cm²