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WGU D128 Mathematics for Elementary Educators
OA Exam 2026/2027 Actual Exam with Verified
Answers and Detailed Rationales
Question 1
What is the length of the missing leg in a right triangle with a hypotenuse
of 25 in. and a leg of 9 in.?
Correct Answer: 4√34 in.
Rationale:
1. Use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.
2. Substitute known values: 9² + b² = 25² → 81 + b² = 625.
3. Solve for b²: b² = 625 − 81 = 544.
4. Simplify √544 = √(16 × 34) = 4√34.
Question 2
What is a scalene triangle?
Correct Answer: No congruent sides.
Rationale:
1. Scalene triangles have all sides of different lengths.
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2. No sides are congruent (equal).
3. No angles are congruent in a scalene triangle.
4. This distinguishes scalene from isosceles (two equal sides) and
equilateral (three equal sides).
Question 3
Find the distance between points (0, 4) and (15, 0) by applying the
Pythagorean theorem.
Correct Answer: 15.52
Rationale:
1. The distance formula is derived from the Pythagorean theorem: d =
√[(x₂−x₁)² + (y₂−y₁)²].
2. Substitute: d = √[(15−0)² + (0−4)²] = √[15² + (−4)²].
3. Calculate: √[225 + 16] = √241.
4. √241 ≈ 15.52.
Question 4
A circle has a diameter of 12.8 ft. What is the area of this circle?
Correct Answer: 128.61 ft²
Rationale:
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1. Radius = diameter ÷ 2 = 12.8 ÷ 2 = 6.4 ft.
2. Area formula: A = πr².
3. A = 3.14 × (6.4)² = 3.14 × 40.96.
4. A = 128.6144 ≈ 128.61 ft².
Question 5
A circle has a circumference of 12.65 cm. Assuming π = 3.14, what is the
measure of this circle's diameter?
Correct Answer: 4.03 cm
Rationale:
1. Circumference formula: C = πd.
2. Solve for diameter: d = C ÷ π.
3. d = 12.65 ÷ 3.14 ≈ 4.0286.
4. Rounded to two decimal places: 4.03 cm.
Question 6
A directional sign can be best described as which type of polygon?
Correct Answer: Rectangle
Rationale:
1. Directional signs are typically rectangular in shape.
WGU D128 Mathematics for Elementary Educators
OA Exam 2026/2027 Actual Exam with Verified
Answers and Detailed Rationales
Question 1
What is the length of the missing leg in a right triangle with a hypotenuse
of 25 in. and a leg of 9 in.?
Correct Answer: 4√34 in.
Rationale:
1. Use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.
2. Substitute known values: 9² + b² = 25² → 81 + b² = 625.
3. Solve for b²: b² = 625 − 81 = 544.
4. Simplify √544 = √(16 × 34) = 4√34.
Question 2
What is a scalene triangle?
Correct Answer: No congruent sides.
Rationale:
1. Scalene triangles have all sides of different lengths.
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2. No sides are congruent (equal).
3. No angles are congruent in a scalene triangle.
4. This distinguishes scalene from isosceles (two equal sides) and
equilateral (three equal sides).
Question 3
Find the distance between points (0, 4) and (15, 0) by applying the
Pythagorean theorem.
Correct Answer: 15.52
Rationale:
1. The distance formula is derived from the Pythagorean theorem: d =
√[(x₂−x₁)² + (y₂−y₁)²].
2. Substitute: d = √[(15−0)² + (0−4)²] = √[15² + (−4)²].
3. Calculate: √[225 + 16] = √241.
4. √241 ≈ 15.52.
Question 4
A circle has a diameter of 12.8 ft. What is the area of this circle?
Correct Answer: 128.61 ft²
Rationale:
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1. Radius = diameter ÷ 2 = 12.8 ÷ 2 = 6.4 ft.
2. Area formula: A = πr².
3. A = 3.14 × (6.4)² = 3.14 × 40.96.
4. A = 128.6144 ≈ 128.61 ft².
Question 5
A circle has a circumference of 12.65 cm. Assuming π = 3.14, what is the
measure of this circle's diameter?
Correct Answer: 4.03 cm
Rationale:
1. Circumference formula: C = πd.
2. Solve for diameter: d = C ÷ π.
3. d = 12.65 ÷ 3.14 ≈ 4.0286.
4. Rounded to two decimal places: 4.03 cm.
Question 6
A directional sign can be best described as which type of polygon?
Correct Answer: Rectangle
Rationale:
1. Directional signs are typically rectangular in shape.
