Tony Stark has a right triangle with a base of 6 feet and a height of 4 feet. If Dr. Banner were to construct a similar but not congruent right triangle with an area of 108 square feet, what would the dimensions of the Dr. Banner's triangle be?

Answers

Answer 1

Answer:

[tex]Base = 18ft[/tex]

[tex]Height = 12ft[/tex]

Explanation:

Given

Triangle 1 (Tony Stark):

[tex]Base = 6ft[/tex]

[tex]Height = 4ft[/tex]

Triangle 2 (Dr. Banner):

[tex]A_2 = 108ft^2[/tex]

Required

Determine the dimensions of the second triangle

The area of a triangle is:

[tex]Area = 0.5 * Base * Height[/tex]

First, calculate the area of Triangle 1

[tex]A_1 = 0.5 * Base * Height[/tex]

[tex]A_1 = 0.5 * 6ft * 4ft[/tex]

[tex]A_1 = 12ft^2[/tex]

Divide the area of Triangle 2 with the area of triangle to get the scale factor (n) of the area.

[tex]n = \frac{A_2}{A_1}[/tex]

[tex]n = \frac{108ft^2}{12ft^2}[/tex]

[tex]n = \frac{108}{12}[/tex]

[tex]n = 9[/tex]

The scale factor (k) of the dimensions of triangle 1 to 2 is the square root of the scale factor of the area (n):

[tex]k = \sqrt{n[/tex]

[tex]k = \sqrt{9[/tex]

[tex]k = 3[/tex]

For triangle 1, we have:

[tex]Base = 6ft[/tex]

[tex]Height = 4ft[/tex]

The dimension of triangle 2 is:

[tex]Base = 3 * 6ft[/tex]

[tex]Base = 18ft[/tex]

[tex]Height = 3 * 4ft[/tex]

[tex]Height = 12ft[/tex]


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