The area of a rectangular garden would be increased by 150 square feet

Let L = the ORIGINAL length of the rectangle
Let W = the ORIGINAL width of the rectangle

So, LW = the ORIGINAL area of the rectangle

The area of a rectangular garden would be increased by 150 square feet if the length were increased by 7.5 feet
So we have the following "word equation": (area of NEW rectangle) - (area of ORIGINAL rectangle) = 150

NEW length = L + 7.5
In this case, the width remains at W
So, the NEW area = (L + 7.5)(W)

Plug values into the word equation to get: (L + 7.5)(W) - LW = 150
Expand: LW + 7.5W - LW = 150
Simplify: 7.5W = 150
Divide both sides by 7.5 to get: W = 20


The area of a rectangular garden would be increased by 150 square feet if the width were increased by 5 feet
Once again, we have the "word equation": (area of NEW rectangle) - (area of ORIGINAL rectangle) = 150

NEW with = W + 5
In this case, the length remains at L
So, the NEW area = (L)(W + 5)

Plug values into the word equation to get: (L)(W + 5) - LW = 150
Expand: LW + 5L - LW = 150
Simplify: 5L = 150
Divide both sides by 5 to get: L = 30

What is the area of the garden, in square feet?
ORIGINAL area of the rectangle = LW
= (30)(20)
= 600

Answer: A

Cheers,
Brent

A.

Let length = l feet
Let breadth = b feet
Area = lb sq feet


Case I:
A + 150 = (l+7.5)b
lb + 150 = lb + 7.5b
150 = 7.5b
=> b = 20 feet

Case II:
A + 150 = l(b+5)
lb + 150 = lb + 5l
150 = 5l
=> l = 30 feet

Area = l*b = 30 * 20 = 600 sqaure feet

We get 2 equations,
(x+7.5) * y = xy + 150 -- 1
x* ( y +5 ) = xy + 150 -- 2

from eq 1, y = 20.
from eq 2, x = 30.
xy ( area ) = 600.
Option A

Let L = the length of the garden and W = the width of the garden. We can create the equations:

(L + 7.5)W = LW + 150

and

L(W + 5) = LW + 150

Solving the first equation, we have:

LW + 7.5W = LW + 150

7.5W = 150

W = 20

Solving the second equation, we have:

LW + 5L = LW + 150

5L = 150

L = 30

Therefore, the area of the garden is 30 x 20 = 600 sq. ft.

Answer: A

Area of rectangle = \(lw\)

If either the length were increased by 7.5 ft or width were increased by 5 ft = area will be increased by 150

\(l(w+5) = lw + 150\)

\(lw + 5l = lw + 150\)

\(l = 30\)

\(w(l+7.5) = lw + 150\)

\(lw + 7.5w = lw + 150\)

\(w = 20\)

\(lw = 20 * 30 = 600\)

Answer is A.

why is D incorrect? if the length is 10 and 30... the answer would still work

why is D incorrect? if the length is 10 and 30... the answer would still work