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.