Question

b. use the triangles below to fill in the table.

(original triangle: base 3 cm, height 4 cm, hypotenuse 5 cm; enlarged triangle: base 9 cm, height 12 cm, hypotenuse 15 cm)

geometric shape	base	height	perimeter	area
enlarged triangle

a. what is the scale factor from the original triangle to the enlarged triangle?

b. what is the scale factor from the enlarged triangle to the original triangle?

Explanation:

Step1: Calculate perimeter and area for original triangle

• Perimeter: Sum of side lengths. \(3 + 4+5=12\) cm.
• Area: Use formula \(A=\frac{1}{2}\times base\times height\). Here, \(base = 3\) cm, \(height = 4\) cm. So \(A=\frac{1}{2}\times3\times4 = 6\) \(cm^{2}\).

Step2: Calculate perimeter and area for enlarged triangle

• Perimeter: Sum of side lengths. \(9 + 12+15=36\) cm.
• Area: Use formula \(A=\frac{1}{2}\times base\times height\). Here, \(base = 9\) cm, \(height = 12\) cm. So \(A=\frac{1}{2}\times9\times12 = 54\) \(cm^{2}\).

Step3: Find scale factor from original to enlarged

Divide corresponding sides (e.g., \(\frac{9}{3}=3\), \(\frac{12}{4}=3\), \(\frac{15}{5}=3\)). Scale factor is \(3\).

Step4: Find scale factor from enlarged to original

Divide corresponding sides (e.g., \(\frac{3}{9}=\frac{1}{3}\), \(\frac{4}{12}=\frac{1}{3}\), \(\frac{5}{15}=\frac{1}{3}\)). Scale factor is \(\frac{1}{3}\).

Answer:

Geometric Shape	Base	Height	Perimeter	Area
Enlarged Triangle	\(9\) cm	\(12\) cm	\(36\) cm	\(54\) \(cm^{2}\)

a. The scale factor from the original triangle to the enlarged triangle is \(3\).

b. The scale factor from the enlarged triangle to the original triangle is \(\frac{1}{3}\).