the diagram shows a child t - shirt and an adult t - shirt, the child t shirt has a width of 12 cm and adult with a width of 16cm. the childs sleeve length is 5 cm. (a) find the scale factor of the enlargment (b) the width of the arm sleeve of the adult
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We have a scale factor problem involving t-shirts. The child t-shirt has a width of 12 centimeters and sleeve length of 5 centimeters. The adult t-shirt has a width of 16 centimeters. We need to find the scale factor of enlargement and the adult sleeve length.
To find the scale factor, we divide the adult width by the child width. The scale factor equals 16 centimeters divided by 12 centimeters, which simplifies to 16 over 12, and further reduces to 4 over 3. Therefore, the scale factor of enlargement is 4 thirds.
To find the adult sleeve length, we multiply the child sleeve length by the scale factor. The adult sleeve length equals 5 centimeters times 4 thirds, which gives us 5 times 4 divided by 3, equals 20 over 3 centimeters. Therefore, the adult sleeve length is 20 thirds centimeters.
Let's summarize our complete solution. For part a, the scale factor is 4 thirds, found by dividing the adult width by the child width. For part b, the adult sleeve length is 20 thirds centimeters, calculated by multiplying the child sleeve length by the scale factor. This demonstrates the key concept that when objects are scaled, all corresponding dimensions are multiplied by the same scale factor.
We have successfully solved this scale factor problem. The scale factor is 4 thirds, and the adult sleeve length is 20 thirds centimeters. Scale factors are widely used in real-world applications including maps, blueprints, photography, engineering design, and computer graphics. The key principle to remember is that when scaling objects, all corresponding dimensions must be multiplied by the same scale factor to maintain proportional relationships.