A house has two rooms of equal area. One room is a rectangle 4ft narrower and 5ft longer then the square one. Find the area of each room.
Please explain to me what to do because i am confused. Thanks
Square room is x by x with area x^2.
The rectangular room is (x - -4) by (x + 5.
Therefore, x^2 = (x-4)(x+5)
I bet you can take it from here.
To solve this problem, we will use some basic algebra. Let's denote the length and width of the square room as "x". This means that its area would be x * x = x^2.
Next, we are given that the rectangular room is 4ft narrower and 5ft longer than the square room. Hence, its length and width would be (x + 5) and (x - 4) respectively. Therefore, the area of the rectangular room would be (x + 5) * (x - 4) = (x^2 + x - 20).
Since we know that both rooms have equal areas, we can equate the two expressions for the areas of the rooms:
x^2 = x^2 + x - 20
By canceling out x^2 from both sides of the equation, we are left with:
0 = x - 20
Adding 20 to both sides, we get:
x = 20
Now that we have found the value of x, we can substitute it back into the expressions for the areas of the rooms to find their actual areas:
Area of the square room = x^2 = 20^2 = 400 square feet
Area of the rectangular room = x^2 + x - 20 = 20^2 + 20 - 20 = 400 square feet
Therefore, the area of each room is 400 square feet.