A picture measuring 18cm by 14cm is placed inside a frame leaving a margin of uniform width all around the picture. The width of the margin is y centimetres and the area of the frame is 320cm square. The margin is covered with velvet material at a cost of sh8.50 per square centimetres
A) draw a sketch of the frame the picture and the margin
B)determine the value of y
C)determine the dimensions of the frame
D)calculate the cost of the material required to cover the margin
A) Here is a sketch of the frame, the picture, and the margin:
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| ___ |
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| y |
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B) To determine the value of y, we need to use the given information:
- The length of the picture is 18cm.
- The width of the picture is 14cm.
- The area of the frame is 320cm square.
Since the length of the frame is equal to the length of the picture plus two margins (on both sides), we can write the equation:
18cm + 2y = length of the frame
Similarly, since the width of the frame is equal to the width of the picture plus two margins (on both top and bottom), we can write the equation:
14cm + 2y = width of the frame
We also know that the area of the frame is 320cm square. The formula for the area of a rectangle is length times width, so we can write the equation:
(length of the frame) * (width of the frame) = 320cm square
Using these three equations, we can solve for y.
C) To determine the dimensions of the frame, we can substitute the value of y into the equations:
18cm + 2y = length of the frame
14cm + 2y = width of the frame
D) To calculate the cost of the material required to cover the margin, we need to determine the area of the margin and then multiply it by the cost per square centimeter (8.50 sh).
The area of the picture is 18cm * 14cm = 252cm square.
The area of the frame is 320cm square.
So, the area of the margin is the difference between the area of the frame and the area of the picture:
Area of margin = Area of frame - Area of picture
Once the area of the margin is determined, we can calculate the cost by multiplying it by the cost per square centimeter (8.50 sh).