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An author is writing and illustrating a new book. The tape diagram represents the ratio of area, in cm 2 cm 2 start text, c, m, end text, squared, with text to area with illustrations. A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Text area. The second tape has 2 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Illustration area. Text areaIllustration area A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Text area. The second tape has 2 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Illustration area. Based on the ratio, what is the area of the text when there are 500 cm 2 500cm 2 500, start text, c, m, end text, squared of illustr

Sagot :

MrRoyal

Tape diagrams are models that used to represent ratios using rectangles

The area on the second tape diagram is 750 square cm

How to determine the ratio

From the tape diagram, we have the following area ratio

[tex]Ratio = 2cm^2 : 3cm^2[/tex]

Rewrite the ratio, as follows:

[tex]First : Second = 2cm^2 : 3cm^2[/tex]

When the area on the first tape is 500 cm^2, the ratio becomes

[tex]500 cm^2 : Second = 2cm^2 : 3cm^2[/tex]

Multiply the ratio on the right side by 250.

So, we have:

[tex]500 cm^2 : Second = 2cm^2 * 250 : 3cm^2 * 250[/tex]

Evaluate the products

[tex]500 cm^2 : Second = 500cm^2 : 750cm^2[/tex]

By comparison, we have:

[tex]Second = 750cm^2[/tex]

Hence, the area on the second tape diagram is 750 square cm

Read more about ratios at:

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