Question

Jesse has 2 similar rectangles. He finds that the larger rectangle has a base of 10 inches and a height of 5 inches. What is the height, in inches, of the smaller rectangle if the base is 4 inches?

Answer 1

Sides of first rectangle are 12 inches and 6 inches

and sides of second rectangle are 10 inches and 5 incheAnswer:

Step-by-step explanation:

Ratio of bases = 12/10 = 6/5

Ratio of altitudes = 6/5

Answer 2

By applying the definition of similar rectangles and proportion, the height of the smaller rectangle is: 2 inches.

Recall:

• Similar rectangles have corresponding dimensions that are proportionate to each other.

• In order words, the ratios of the corresponding dimensions of similar triangles are equal.

Thus:

• Base of larger rectangle = 10 inches
• Height of larger rectangle = 5 inches
• Base of smaller rectangle = 4 inches
• Let the height of the smaller rectangle be represented as x

We will have the following proportion:

$\frac{10}{4} = \frac{5}{x}$

• Cross multiply and find x

$x = \frac{20}{10} \\\\\mathbf{x = 2}$

The height of the smaller rectangle is 2 inches.

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