Measurement and Geometry

1. Kilometers to meters:

$5 \text{ km} \times 1{,}000 \text{ m/km} = 5{,}000 \text{ m}$

The relay race is $5{,}000$ meters long.

Kilograms to grams:

$3 \text{ kg} \times 1{,}000 \text{ g/kg} = 3{,}000 \text{ g}$

The bag of apples weighs $3{,}000$ grams.

2. Convert the hours to minutes, then add the remaining minutes:

$2 \text{ hours} \times 60 \text{ min/hour} = 120 \text{ minutes}$

$120 + 15 = 135 \text{ minutes}$

The whole movie is $135$ minutes.

3. Perimeter is the distance around the garden:

$P = 2 \times (12 + 8) = 2 \times 20 = 40 \text{ feet}$

Area is the space inside the garden:

$A = 12 \times 8 = 96 \text{ square feet}$

4. The perimeter of a rectangle is $P = 2 \times (\text{length} + \text{width})$.

We know $P = 40$ m and length $= 12$ m:

$40 = 2 \times (12 + w)$

$20 = 12 + w$

$w = 20 - 12 = 8$

The pen can be $8$ meters wide.

The area of the pen:

$A = 12 \times 8 = 96 \text{ square meters}$

5. a) Square. A square has 4 equal sides and 4 right angles. It has 2 pairs of parallel sides (opposite sides are parallel) and perpendicular sides (sides that meet at right angles). So it has both parallel and perpendicular sides.

b) Right triangle. A triangle with one right angle. Triangles have no parallel sides. The two sides that form the right angle are perpendicular to each other.

c) Parallelogram (specifically a rhombus if all sides are equal, or a general parallelogram). It has 2 pairs of parallel sides, but since there are no right angles, it has no perpendicular sides.