how about this?

Question

A house has two rooms of equal area. One room is square and the other room a rectangle, 4 ft narrower and 5 ft longer than the square one. Find the area of each room.
A.
289 ft2

B.
324 ft2

C.
400 ft2

D.
382 ft2

Answer 1

Let

x² = sides of the square room

(x - 4) = 4 feet narrow side of the rectangle

(x + 5) = 5 feet longe side of the rectangle

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x² = (x + 5)(x - 4)=

x² = x² + 5x - 4x - 20

x² = x² + x - 20

x² - x² = x² + x - 20 - x²

x - 20 = 0

x - 20 + 20 = 0 + 20

x = 20

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Since the area fo the square room is x²

x = 20

20 x 20 = 400

The area of the square room is 400 square feet

The answer is c 400 square feet

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Answer 2

The sides of the square room are each of length x.
The sides of the rectangular room are of length (x-4) and (x+5).

The area of the first room is x*x
The area of the second room is (x-4)*(x+5)
They equal each other, so x^2 = (x-4)*(x+5)
Expand this to get x^2 = x^2 + x - 20
Subtract x^2 from both sides
0 = x - 20
Add 20 to both sides
20 = x
Using this, the area of the first room is 20*20 = 400.
Also, the area of the second room is 16*24 = 400.

The area of both rooms is 400 ft^2

I hope this helps!

Answer 3

Square room:
Length of each wall = X
Area of the room = X^2

Rectangular room:
Length of one wall = X – 4
Length of another wall = X + 5
Area of the room = (X – 4) * (X + 5)

As both rooms have the same area,

X^2 = (X – 4) * (X + 5)

X^2 = X^2 – 4X + 5X – 20

X^2 – X^2 – 4X + 5X = 20

X = 20

X^2 = 400

Area = 400

Answer: C

Answer 4

400 ft2

Answer 5

(x-4)(x+5)=x^2
x^2-20+x=x^2
x=20
the rectangle=16*25
area=400sft
squar=20*20
area=400 sft

Answer 6

x^2=(x+5)(x-4)
x^2=x^2+x-20
0=x-20
x=20
A=S^2
A=20^2
A=400