1. A rectangular wooden frame has side lengths 5x and 7x + 1. The rectangular opening for a picture has side lengths 3x and 5x.
-What is the area of the wooden part of the frame? Write your answer in factored form.
-How can drawing a diagram help you solve the problem?
-How can you express the area of the wooden part of the frame as a difference of areas?
2. Describe and correct the error made in multiplying.
I need help with the first one, I know it a little bit but any guidance would be great. But I have no clue what the second one is asking:( Thx!
For the first one, this is the equation i got:
5x * 7x (+1) - 3x * 5x
is this correct?
is 20x^2 correct?
How do i say the other parts?
And i still have no clue was #2 is trying to ask:(
(5x)(7x+1)-(3x)(5x) = (7x+1-3x)(5x) = (4x+1)(5x)
1. To find the area of the wooden part of the frame, we need to subtract the area of the rectangular opening from the area of the entire frame.
Let's start by finding the area of the entire frame. The length of the frame is 5x and the width is 7x + 1. So, the area of the entire frame can be calculated as:
Area of the frame = Length × Width
= (5x) × (7x + 1)
= 35x^2 + 5x
Next, we need to find the area of the rectangular opening. The length of the opening is 3x and the width is 5x. So, the area of the opening can be calculated as:
Area of the opening = Length × Width
= (3x) × (5x)
= 15x^2
Now, to find the area of the wooden part of the frame, we subtract the area of the opening from the area of the frame:
Area of wooden part of the frame = Area of the frame - Area of the opening
= (35x^2 + 5x) - (15x^2)
= 35x^2 + 5x - 15x^2
= 20x^2 + 5x
Thus, the area of the wooden part of the frame is 20x^2 + 5x, written in factored form.
Drawing a diagram can help you visualize the problem and understand the relationship between different lengths and areas. Drawing a rectangle for the frame and another rectangle for the opening can give a clear visual representation of the problem. It can help you see the lengths involved and how to calculate the areas.
To express the area of the wooden part of the frame as a difference of areas, we can think of it as the area of the frame minus the area of the opening. This allows us to represent the wooden part as the difference between the two areas, which are calculated separately.