Question

homework for 3.1.4
3 - 46 juan bobo is resizing an image of a coqui for a presentation.
what is preserved (remains the same) about the pre - image and the new image?
why is the new image not a rigid transformation?
3 - 47 the perimeter of the triangle at right is 52 units.
write and solve an equation based on the information in the diagram.
use your solution for x to calculate the length of each side of the triangle.
be sure to confirm that your answer is correct.

Explanation:

Step1: Set up the equation for the perimeter

The perimeter of a triangle is the sum of its sides. So, \( (7x - 4)+19+(10x + 3)=52 \).
Simplify the left - hand side: \( 7x-4 + 19+10x + 3=(7x+10x)+(-4 + 19+3)=17x + 18 \).
The equation becomes \( 17x+18 = 52 \).

Step2: Solve for \( x \)

Subtract 18 from both sides: \( 17x+18-18=52 - 18 \), so \( 17x=34 \).
Divide both sides by 17: \( x=\frac{34}{17}=2 \).

Step3: Calculate the length of each side

For the side \( 7x - 4 \), substitute \( x = 2 \): \( 7\times2-4=14 - 4=10 \).
For the side \( 10x + 3 \), substitute \( x = 2 \): \( 10\times2+3=20 + 3=23 \).
The third side is 19.

Step4: Confirm the answer

Check the perimeter: \( 10 + 19+23=52 \).

Answer:

\( x = 2 \), the side lengths are 10 units, 19 units, and 23 units.