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

Answer:

$Base = 18ft$

$Height = 12ft$

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.

$n = \frac{A_2}{A_1}$

$n = \frac{108ft^2}{12ft^2}$

$n = \frac{108}{12}$

$n = 9$

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:

$Base = 3 * 6ft$

$Base = 18ft$

$Height = 3 * 4ft$

$Height = 12ft$