GED Mathematical reasoning 2 — Questions and Answers

Question 1: A rectangle has a length of 12 cm and a width of 7 cm. What is its perimeter?

19 cm
38 cm (Correct answer)
84 cm
76 cm

Correct answer: 38 cm

Perimeter of a rectangle = 2(length + width) = 2(12 + 7) = 2(19) = 38 cm.

The perimeter of a rectangle is the total length of all four sides. Formula: P = 2l + 2w = 2(l + w) where l = length and w = width. P = 2(12 + 7) = 2(19) = 38 cm You can also add all four sides directly: 12 + 7 + 12 + 7 = 38 cm ✓ Don't confuse perimeter (distance around) with area (space inside): • Perimeter = 38 cm (linear measurement) • Area = 12 × 7 = 84 cm² (square measurement) Option C (84 cm) is the area, not the perimeter — a common mistake on the GED.

Question 2: Find the area of a triangle with a base of 10 inches and a height of 6 inches.

16 sq in
30 sq in (Correct answer)
60 sq in
120 sq in

Correct answer: 30 sq in

Area of triangle = (1/2) × base × height = (1/2) × 10 × 6 = 30 square inches.

The area of a triangle formula is: A = ½ × b × h, where b is the base and h is the perpendicular height. A = ½ × 10 × 6 = ½ × 60 = 30 square inches. The formula makes geometric sense: a triangle is half of a parallelogram (or rectangle for right triangles) with the same base and height. If you draw two congruent triangles together along their bases, they form a rectangle of area b × h, so each triangle has area ½bh. Important: the height must be PERPENDICULAR to the base — it's not necessarily the slant side of the triangle. Units: area is always expressed in square units (in², cm², ft², etc.).

Question 3: What is the volume of a rectangular box (prism) with length 5 ft, width 4 ft, and height 3 ft?

12 ft³
47 ft³
60 ft³ (Correct answer)
120 ft³

Correct answer: 60 ft³

Volume of a rectangular prism = l × w × h = 5 × 4 × 3 = 60 cubic feet.

Volume measures the three-dimensional space inside a solid figure. For a rectangular prism (box): V = l × w × h V = 5 × 4 × 3 = 60 ft³ You can think of it as: (area of base) × height = (5 × 4) × 3 = 20 × 3 = 60 ft³. Volume is expressed in cubic units (ft³, cm³, m³, etc.) because you're multiplying three length measurements. Real-world application: This box could hold 60 cubic feet of material. If you were filling it with 1-foot cubes, you'd need exactly 60 of them. Don't confuse with surface area: SA = 2(lw + lh + wh) = 2(20 + 15 + 12) = 2(47) = 94 ft².

Question 4: In a right triangle, the two legs measure 6 cm and 8 cm. What is the length of the hypotenuse?

7 cm
10 cm (Correct answer)
11 cm
14 cm

Correct answer: 10 cm

Using the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.

The Pythagorean theorem states that in any right triangle, the sum of the squares of the two legs equals the square of the hypotenuse: a² + b² = c². c² = 6² + 8² = 36 + 64 = 100 c = √100 = 10 cm This is a 3-4-5 Pythagorean triple scaled up by 2: (6, 8, 10) = 2×(3, 4, 5). Recognizing common Pythagorean triples saves time on the GED: • 3-4-5 (and multiples: 6-8-10, 9-12-15) • 5-12-13 • 8-15-17 The hypotenuse is always the longest side and is opposite the right angle (90° angle). Always check that your answer is larger than both legs.

Question 5: A circular pond has a radius of 7 meters. Using π ≈ 3.14, what is the area of the pond?

21.98 m²
43.96 m²
153.86 m² (Correct answer)
615.44 m²

Correct answer: 153.86 m²

Area = π × r² = 3.14 × 7² = 3.14 × 49 = 153.86 m².

The area of a circle is A = πr², where r is the radius. A = π × r² = 3.14 × 7² = 3.14 × 49 = 153.86 m² Common mistakes: • Using diameter instead of radius: if the diameter were 7, r = 3.5, and A = 3.14 × 12.25 ≈ 38.5 m² • Forgetting to square: 3.14 × 7 = 21.98 (that's approximately the circumference ÷ 2) Related formula — circumference: C = 2πr = 2 × 3.14 × 7 = 43.96 m (option B is this value) Memory trick: 'Area = πr²' — think 'a pie are squared' to remember the formula.

Question 6: Two angles of a triangle measure 55° and 72°. What is the measure of the third angle?

33°
53° (Correct answer)
63°
127°

Correct answer: 53°

The sum of angles in a triangle is 180°. Third angle = 180° − 55° − 72° = 53°.

The Triangle Angle Sum Theorem states that the interior angles of any triangle always sum to 180°. Third angle = 180° − 55° − 72° = 180° − 127° = 53°. Verification: 55° + 72° + 53° = 180° ✓ This is a fundamental geometric property that applies to ALL triangles — equilateral, isosceles, scalene, right, acute, and obtuse. Note: For polygons with more sides, the angle sum formula is (n − 2) × 180°, where n is the number of sides: • Triangle (n=3): (3−2) × 180° = 180° • Quadrilateral (n=4): (4−2) × 180° = 360° • Pentagon (n=5): (5−2) × 180° = 540°

GED Mathematical reasoning 2

A rectangle has a length of 12 cm and a width of 7 cm.
What is its perimeter?