Question

(a)The perimeter of a rectangular garden is 306m.If the width of the garden is 69m, what is its length?Length of the garden: m (b)The area of a rectangular window is 6364cm2.If the length of the window is 86cm, what is its width?Width of the window: cm

Answer 1

The length of the garden = 84 m

Step-by-step explanation

Part (a)

The given parameters are:

Perimeter of the rectangular garden = 306 m

The width of the garden = 69 m

The length of the garden = ?

Solution:

Using the formula for the perimeter of a rectangle:

`\begin{gathered} Perimeter=2(Length+Width \\ \\ 306m=2(L+69m) \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ \\ (306m)/(2)=(2(L+69m))/(2) \\ \\ 153m=L+69m \\ \\ L=153m-69m \\ \\ L=84\text{ }m \end{gathered}`

The length of the garden = 84 m

Part (b):

The given parameters are:

The area of the rectangular window = 6364 cm²

The length of the window = 86 cm

The width of the window = ?

Solution:

The width of the rectangular window can be calculated using the formula for the area of a rectangle.

`\begin{gathered} Area=Length* Width \\ \\ 6364cm^2=86cm* W \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }86cm \\ \\ (6364cm^2)/(86cm)=(86cm* W)/(86cm) \\ \\ W=74\text{ }cm \end{gathered}`

The width of the window = 74 cm