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.
(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.
well, I do not know which is x and which is y so I will call them w and L
50 = 2 w + L
so L = 50 - 2 w
or
w = (50-L)/2
A = w L = [(50-L)/2]L = 25 L - L^2/2
or
A = (50 - 2w)w = 50 w - 2 w^2
since I do not know which is x, I can not help with c
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.
ok so w = x = 10
A = 50 w -2 w^2 = 50 x - 2 x^2
= 50(10) - 2(100)
= 500 - 200
= 300 m^2
(a) To write an expression for y in terms of x, we need to understand the dimensions of the rectangular garden. Let's assume the length of the garden is x meters and the width is y meters.
Since Mrs. Harvey only needs to fence 3 sides, we can infer that the length of the garden corresponds to the side she needs to fence. Therefore, the length of the garden is x meters, and we can say y meters is the width of the garden.
So, the expression for y in terms of x is: y = x.
(b) To find the expression for the area, we can use the formula for the area of a rectangle, which is given by: Area = length × width.
In this case, the length is x meters, and the width is y meters. As we already found in part (a), y = x. So, we can substitute y with x in the formula:
A = x × x
A = x^2
Therefore, the expression for the area (A) of the garden in terms of x is A = x^2.
(c) If x is 10m, we can use the expression for the area from part (b) to find the area of the garden:
A = x^2
A = 10^2
A = 100 square meters
So, if x is 10 meters, the area of the garden is 100 square meters.