Question

a contractor is designing a new tennis court and creates a blueprint of the court for planning purposes. the actual length of the tennis court is 112 feet, and the length of the court on the blueprint is 16 inches. what is the scale factor used on the blueprint, in feet per inch? while working on a roof design, you found that one of the support beams had been misplaced. to replace it, you needed a smaller triangle with the same shape but different size. give me an example of a similar triangle to the one below but smaller. (triangle with sides 6 cm, 12 cm, 15 cm labeled q, s, r) teks 7.4a use this information to complete the 3 different representations below: a caterpillar crawls 30 inches in 1 hours at a steady pace. create a graph to represent y, the number of inches the caterpillar traveled in x hours. (graph with distance (in.) and time (h) axes) complete the table based on the caterpillar’s movement. time (x) distance (y) 1 hour 30 inches write an equation to represent y, the number of inches the caterpillar traveled in x hours.

Explanation:

First Sub - Question (Tennis Court Scale Factor)

Step 1: Recall Scale Factor Definition

The scale factor (in feet per inch) is the ratio of the actual length to the length on the blueprint. Let \( \text{actual length} = 112\) feet and \( \text{blueprint length}=16\) inches.

Step 2: Calculate the Scale Factor

We calculate the scale factor \( k=\frac{\text{actual length}}{\text{blueprint length}}=\frac{112}{16}\)
\( \frac{112}{16} = 7\)

To find a similar triangle, we can use a scale factor less than 1. The original triangle has sides 6 cm, 12 cm, and 15 cm. Let's use a scale factor of \( \frac{1}{2}\). Multiply each side by \( \frac{1}{2}\): \( 6\times\frac{1}{2}=3\) cm, \( 12\times\frac{1}{2} = 6\) cm, \( 15\times\frac{1}{2}=7.5\) cm. So a triangle with sides 3 cm, 6 cm, and 7.5 cm is similar (same shape, smaller size) to the original triangle.

Step 1: Identify the Relationship

The caterpillar crawls at a constant rate, so the relationship between distance \( y\) (in inches) and time \( x\) (in hours) is linear, \( y = 30x\).

Step 2: Plot Points

For \( x = 0\), \( y=0\); for \( x = 1\), \( y = 30\); for \( x=2\), \( y=60\); for \( x = 3\), \( y = 90\); for \( x=4\), \( y = 120\); for \( x=5\), \( y=150\). Plot these points \((0,0)\), \((1,30)\), \((2,60)\), \((3,90)\), \((4,120)\), \((5,150)\) on the graph with time on the x - axis and distance on the y - axis and draw a straight line through them.

Table:

Answer:

The scale factor is 7 feet per inch.

Second Sub - Question (Similar Triangle)