G7 UNIT 1 REVIEW

By what scale factor is Triangle 1 reduced to form Triangle 2?

• 0.25

• 0.5

• 1.25

• 2.5

Answer explanation

Triangle 1 is reduced to Triangle 2 by a scale factor of 0.5, meaning each side of Triangle 1 is halved to form Triangle 2. This confirms that the correct answer is 0.5.

An architect builds a scale model of a building, where 1 cm = 0.5 m. If the scale model is 15 cm tall,

how tall will the actual building be, in meters, written as a decimal?

Answer explanation

Since 1cm is to 0.5m,

then, 15cm is to 7.5m

(solution: mutltiply15cm by 0.5)

• 46 inches

• 32 inches

Answer explanation

To find the drawing length, convert the actual length of the porch (11.5 ft) to inches: 11.5 ft x 12 in/ft = 138 in. Using the scale (1 in = 4 ft), divide by 4: 138 in / 4 = 34.5 in. The closest answer is 2 7/8 inches.

Mary builds a model of a 120 meter tall building. The height of the model is 60 cm. What is the scale of

the model Mary built?

• 1 cm = 3 m

• 2cm=2m

• 1cm=2m

• 2.5cm=4m

Answer explanation

To find the scale, divide the actual height (120 m) by the model height (0.6 m). This gives a scale of 120 m / 0.6 m = 200, which simplifies to 1 cm = 2 m. Thus, the correct choice is 1 cm = 2 m.

A rectangle, with dimensions labeled, is shown in the diagram. If the lengths of all 4 sides of the rectangle are doubled, then the area will___________.

• double

• increase by 3

• quadruple

• triple

Answer explanation

When the lengths of all sides of a rectangle are doubled, the new area becomes 2L x 2W = 4LW, which is four times the original area. Therefore, the area will quadruple.

Josh made a scale drawing of a square park, which has a side length of 30 feet.

He used the scale 3centimeters = 5 feet.

What will be the area of the scale drawing?

• 324 cm²

• 150 cm²

• 240 cm²

• 600 cm²

Answer explanation

To find the area of the scale drawing, first convert the side length: 30 feet = (30/5)*3 = 18 cm. The area is then 18 cm * 18 cm = 324 cm². Thus, the correct answer is 324 cm².

Maria makes a scale model of her school cafeteria. Her scale is

1cm = 5ft.

What are the actual dimensions of Maria’s school cafeteria?

• 30 ft by 37.5 ft

• 7.5 ft by 90 ft

• 15 ft by 90 ft

• 2.4 ft by 9.5 ft

Answer explanation

Maria's scale of 1cm = 5ft means that to find the actual dimensions, we multiply the model dimensions by 5. The correct choice, 30 ft by 37.5 ft, corresponds to a model size of 6cm by 7.5cm.

A rectangular wall is 5 feet high and 25 feet wide. Which dimensions could be used to represent the

scale drawing?

• 1 inch high and 5 inches wide

• 1 inch high and 25 inches wide

• 5 inches high and 25 inches wide

• 25 inches high and 5 inches wide

Answer explanation

The scale drawing must maintain the same ratio as the original dimensions. The correct choice, 1 inch high and 5 inches wide, keeps the ratio of height to width (5:25) consistent, simplifying to 1:5.

Consider the scale drawing of a triangular garden.

If the actual base of the triangle is 8 meters, what is the actual area of the garden?

• 10 square meters

• 20 square meters

• 40 square meters

• 80 square meters

Answer explanation

To find the area of a triangle, use the formula: Area = 1/2 * base * height. If the base is 8 meters and the height is 10 meters, then Area = 1/2 * 8 * 10 = 40 square meters. Thus, the correct answer is 40 square meters.

If the quadrilateral is enlarged by a scale factor of 3, what will be the new perimeter?

• P = 52.2 ft

• P = 157.2 ft

• P = 193.2 ft

• P = 1, 512 ft

Answer explanation

To find the new perimeter after enlarging by a scale factor of 3, multiply the original perimeter (52.4 ft) by 3. Thus, 52.4 ft x 3 = 157.2 ft, making the correct answer P = 157.2 ft.