Mrs Harvey Wants To Put a 50 m Long Fence around Her Rectangular Garden. She Only Needs To Fence In 3 Sides Because The Other Side Is Alongside Her House.
y=length
x=width
(a) Write an Expression For y In Terms of x
(b) Write an Expression For The Area ( A ) Of The Garden , In Terms of x
(c) If x is 10m, find the area of the garden.
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(a) The expression for y in terms of x can be written as:
y = 50 - 2x
Since the garden fence needs to be placed along three sides, we subtract twice the width (2x) from the total length of the fence (50m) to find the remaining length for the other side.
(b) The expression for the area (A) of the garden in terms of x can be found by multiplying the length and width:
A = x * y
Substituting the expression for y from part (a), we get:
A = x * (50 - 2x)
(c) To find the area of the garden when x is 10m, we substitute x = 10 into the expression from part (b):
A = 10 * (50 - 2 * 10)
= 10 * (50 - 20)
= 10 * 30
= 300 square meters
Therefore, when x is 10m, the area of the garden is 300 square meters.