This Math Geometry section of the LET General Education exam covers 6 expert-reviewed practice questions. Each question has a plain-English explanation and notes on why the wrong answers are wrong.
Sample 1
A square has an area of 400 sq. cm . What is its perimeter?
- A 20 cm
- B 80 cm✓
- C 100 cm
- D 40 cm
Answer: B
A square has 4 equal sides. Its area is found by multiplying one side by itself: side × side.
If the area is 400, then side × side = 400. The number that multiplies by itself to give 400 is 20 (because 20 × 20 = 400). So one side is 20 cm.
The perimeter is the total distance around the square — all 4 sides added up: 4 × 20 = 80 cm.
Tip: For multi-step problems, re-read the question after each step. It's easy to find the side (20 cm) and stop — but the question asked for the perimeter (80 cm).
Why the other choices are wrong
- A. 20 cm is the side length, not the perimeter.
- C. 100 cm would be 5 × 20 — a square has 4 sides, not 5.
- D. 40 cm would be 2 × 20 — that's only two sides.
Sample 2
The smallest angle of a triangle is two-thirds the size of the middle angle, and the middle angle is three-sevenths of the largest angle. Find all three angle measures.
- A 30°, 60°, 90°
- B 45°, 45°, 90°
- C 35°, 45°, 110°
- D 30°, 45°, 105°✓
Answer: D
A triangle's angles always sum to 180°. The numbers in option D — 30°, 45°, 105° — add to 180°, and they fit the size rules: smallest is two-thirds of middle (30 = ⅔ × 45), middle is three-sevenths of largest (45 = ³⁄₇ × 105). The other options fail one or both checks.
Tip: When math options give specific values, plug them in and verify against the rules — often faster than building the equation from scratch.
Why the other choices are wrong
- A. 30+60+90 = 180, but 30 is not 2/3 of 60? Actually 30 IS 2/3 of 45, not 60. And 60 is not 3/7 of 90 (which would need 90×3/7 = 38.6).
- B. 45+45+90 = 180, but the angles must be different (smallest, middle, largest), not two equal.
- C. 35+45+110 = 190, which doesn't even add up to 180 degrees.
Sample 3
A wood frame for pouring concrete has an interior perimeter of 14 meters. Its length is one meter greater than its width. The frame is to be braced with twelve-gauge steel cross-wires. Assuming an extra half-meter of wire is used at either end of a cross-wire for anchoring, what length of wire should be cut for each brace?
Answer: A
First, find the sides: Perimeter is 14, and length is 1m longer than width. The sides must be 3m and 4m. To brace a frame, you go diagonally corner-to-corner. Using the famous 3-4-5 triangle rule, the diagonal is exactly 5 meters. Add 0.5 meters to both ends for tying it down (1 meter total). 5 + 1 = 6 meters.
Tip: Watch for the hidden 3-4-5 right triangle in geometry word problems — it skips the Pythagorean calculation.
Why the other choices are wrong
- B. 7m would be wrong — the diagonal of a 3x4 rectangle is exactly 5, plus 1 anchor = 6m.
- C. 8m is too long — that would mean the diagonal is 7, but it's only 5.
- D. 12m is way too long — that's nearly the whole perimeter, not a brace.
