1. **Problem Statement:** Given two similar quadrilaterals ABCD and EFGH with ABCD ~ EFGH, perimeter of ABCD is 60 inches, area of ABCD is 162 in^2, and some side lengths are given. We need to find: a. Scale factor from ABCD to EFGH b. Length of side EH c. Length of side AB d. Perimeter of EFGH e. Area of EFGH 2. **Important formulas and rules:** - For similar figures, the ratio of corresponding side lengths is the scale factor $k$. - The ratio of perimeters is also $k$. - The ratio of areas is $k^2$. 3. **Find the scale factor $k$:** From the diagram, side EF in EFGH corresponds to side AB in ABCD. Given EF = 6. We need AB to find $k$, but AB is unknown. However, we have other sides: AD = 24 in (ABCD), GH = 10 in (EFGH), and DC = 15 in (ABCD). Since GH corresponds to DC, we can find $k$ as: $$k = \frac{\text{length in EFGH}}{\text{corresponding length in ABCD}} = \frac{10}{15} = \frac{2}{3}$$ 4. **Find EH:** EH corresponds to AD. Given AD = 24 in. So, $$EH = k \times AD = \frac{2}{3} \times 24 = 16$$ 5. **Find AB:** AB corresponds to EF. Given EF = 6. So, $$AB = \frac{EF}{k} = \frac{6}{\frac{2}{3}} = 6 \times \frac{3}{2} = 9$$ 6. **Find perimeter of EFGH:** Perimeter of ABCD = 60 in. Perimeter of EFGH = $k \times$ Perimeter of ABCD $$= \frac{2}{3} \times 60 = 40$$ 7. **Find area of EFGH:** Area of ABCD = 162 in$^2$. Area ratio = $k^2 = \left(\frac{2}{3}\right)^2 = \frac{4}{9}$ Area of EFGH = $k^2 \times$ Area of ABCD $$= \frac{4}{9} \times 162 = 72$$ **Final answers:** - a. Scale factor $k = \frac{2}{3}$ - b. $EH = 16$ in - c. $AB = 9$ in - d. Perimeter of EFGH = 40 in - e. Area of EFGH = 72 in$^2$