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 rectangle is 4 times as long as it is wide. Which of the following could be its dimensions (width × length)?
- A 2 x 32
- B 4 x 16✓
- C 3 x 14
- D 5 x 12
Answer: B
If the rectangle is 4 times as long as it is wide, then length = 4 × width. Only 4 × 16 fits: width = 4, length = 16, and 16 = 4 × 4.
Tip: When a problem gives a simple ratio rule, divide each option's bigger number by its smaller number — only one will match the required multiplier.
Why the other choices are wrong
- A. 2 × 32: 32 = 16 × 2, so length would be 16 times the width, not 4 times.
- C. 3 × 14: 14 ÷ 3 ≈ 4.67, not exactly 4 times.
- D. 5 × 12: 12 ÷ 5 = 2.4, not 4 times.
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 two-thirds of 60 (that would be 40), and 60 is not three-sevenths of 90 (that would be about 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.
