Question

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?

Answer 1

`Base = 18ft`

`Height = 12ft`

Step-by-step explanation:

Given

Triangle 1 (Tony Stark):

`Base = 6ft`

`Height = 4ft`

Triangle 2 (Dr. Banner):

`A_2 = 108ft^2`

Required

Determine the dimensions of the second triangle

The area of a triangle is:

`Area = 0.5 * Base * Height`

First, calculate the area of Triangle 1

`A_1 = 0.5 * Base * Height`

`A_1 = 0.5 * 6ft * 4ft`

`A_1 = 12ft^2`

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

`n = (A_2)/(A_1)`

`n = (108ft^2)/(12ft^2)`

`n = (108)/(12)`

`n = 9`

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

`k = \sqrt{n`

`k = \sqrt{9`

`k = 3`

For triangle 1, we have:

`Base = 6ft`

`Height = 4ft`

The dimension of triangle 2 is:

`Base = 3 * 6ft`

`Base = 18ft`

`Height = 3 * 4ft`

`Height = 12ft`