Question

grade 8 math mystery assignment 11.3
multiple choice (7 questions)

1. a triangle has a base of 12 cm and a height of 6 cm. what is its area?

a. 18 cm²
b. 36 cm²
c. 72 cm²
d. 144 cm²

1. a rectangle has a length of 3.5 meters and a width of 2 meters. what is its area in square centimeters?

a. 350 cm²
b. 700 cm²
c. 7,000 cm²
d. 70,000 cm²

1. the ratio of cats to dogs in a shelter is 5:3. if there are 40 animals total, how many cats are there?

a. 15
b. 20
c. 25
d. 30

1. a smoothie recipe uses 4 cups of fruit for every 3 cups of yogurt. how many cups of yogurt are needed for 12 cups of fruit?

a. 6
b. 8
c. 9
d. 10

1. a map scale is 1 inch : 8 miles. how many miles apart are two towns that are 2.5 inches apart on the map?

a. 10 miles
b. 16 miles
c. 18 miles
d. 20 miles

Explanation:

Step1: Calculate area of triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Given \(b = 12\) cm and \(h=6\) cm.
\(A=\frac{1}{2}\times12\times6\)

Step2: Simplify the expression

\(\frac{1}{2}\times12\times6=( \frac{12}{2})\times6 = 6\times6=36\) \(cm^{2}\)

Step3: Calculate area of rectangle in meters then convert to centimeters

The formula for the area of a rectangle is \(A = lw\). Given \(l = 3.5\) m and \(w = 2\) m. \(A=3.5\times2 = 7\) \(m^{2}\). Since \(1\) \(m^{2}=10000\) \(cm^{2}\), then \(7\times10000 = 70000\) \(cm^{2}\)

Step4: Use ratio to find number of cats

The ratio of cats to dogs is \(5:3\), so the total ratio parts is \(5 + 3=8\). If there are \(40\) animals total, each part is \(\frac{40}{8}=5\). The number of cats is \(5\times5 = 25\)

Step5: Set up proportion for smoothie recipe

Let \(x\) be the cups of yogurt. The proportion is \(\frac{4}{3}=\frac{12}{x}\). Cross - multiply: \(4x=3\times12\), \(4x = 36\), \(x=\frac{36}{4}=9\)

Step6: Use map scale to find distance

If \(1\) inch represents \(8\) miles, for \(2.5\) inches. The distance \(d=2.5\times8=(2 + 0.5)\times8=2\times8+0.5\times8=16 + 4=20\) miles

Answer:

1. B. \(36\) \(cm^{2}\)
2. D. \(70,000\) \(cm^{2}\)
3. C. \(25\)
4. C. \(9\)
5. D. \(20\) miles