Word Problems and Operations #1
SOLUTIONS:
1.
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width)
In this case, the perimeter is given as 50 cm, so we can set up the equation: 50 cm = 2((2w - 2 cm) + w)
Simplifying the equation, we have:
50 cm = 2(3w - 2 cm)
50 cm = 6w - 4 cm
54 cm = 6w
Dividing both sides of the equation by 6, we get: w = 9 cm
Therefore, the width of the rectangle is 9 cm.
2.
Let's denote the shortest side of the triangle as "x" cm. According to the given information, one side of the triangle is 3 cm longer than the shortest side, and the other side is 4 cm longer than the shortest side. This can be expressed as:
Side 1 = x + 3 cm
Side 2 = x + 4 cm
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as 67 cm, so we can set up the equation:
67 cm = x + (x + 3 cm) + (x + 4 cm)
Simplifying the equation, we have:
67 cm = 3x + 7 cm
Subtracting 7 cm from both sides of the equation, we get:
60 cm = 3x
Dividing both sides of the equation by 3, we get:
x = 20 cm
Therefore, the shortest side of the triangle is 20 cm.
3.
To find the number of 1-cm square stickers needed to cover the photo box, we need to calculate the total surface area of the box and then divide it by the area of each sticker.
The surface area of a rectangular box can be found by adding the areas of all its sides. In this case, the photo box has six sides:
Top and bottom sides: 4 cm * 3 cm = 12 cm² each (2 sides total).
Front and back sides: 4 cm * 5 cm = 20 cm² each (2 sides total).
Left and right sides: 3 cm * 5 cm = 15 cm² each (2 sides total).
To calculate the total surface area, we sum up all the side areas:
Total surface area = 2 * (12 cm²) + 2 * (20 cm²) + 2 * (15 cm²)
= 24 cm² + 40 cm² + 30 cm²
= 94 cm²
Now, to determine the number of 1-cm square stickers needed, we divide the total surface area of the box by the area of each sticker:
Number of stickers = Total sur
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