The length of the base of a certain parallelogram is 89% of the height of the parallelogram. Which expression represents...

1. TRANSLATE the problem information

• Given information:
  • Base length = 89% of height
  • \(\mathrm{h}\) = height of parallelogram
  • Need to find: expression for base length

2. TRANSLATE the percentage to decimal form

• Convert 89% to decimal:
  \(\mathrm{89\%}\) = \(\mathrm{89/100}\) = \(\mathrm{0.89}\)

• The phrase "89% of the height" means:
  \(\mathrm{0.89 \times h}\) = \(\mathrm{0.89h}\)

3. Verify by checking what each answer choice represents

• A. \(\mathrm{89h}\) = \(\mathrm{8900\%}\) of \(\mathrm{h}\) (far too large)
• B. \(\mathrm{0.089h}\) = \(\mathrm{8.9\%}\) of \(\mathrm{h}\) (one decimal place off)
• C. \(\mathrm{8.9h}\) = \(\mathrm{890\%}\) of \(\mathrm{h}\) (missing decimal point)
• D. \(\mathrm{0.89h}\) = \(\mathrm{89\%}\) of \(\mathrm{h}\) ✓

Answer: D. \(\mathrm{0.89h}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students struggle with percentage-to-decimal conversion

Many students incorrectly convert \(\mathrm{89\%}\) by either:

• Dropping the percent sign entirely (thinking \(\mathrm{89\%}\) = \(\mathrm{89}\))
• Moving the decimal point the wrong direction (thinking \(\mathrm{89\%}\) = \(\mathrm{0.089}\) instead of \(\mathrm{0.89}\))
• Placing the decimal incorrectly (thinking \(\mathrm{89\%}\) = \(\mathrm{8.9}\))

This leads them to select Choice A (\(\mathrm{89h}\)), Choice B (\(\mathrm{0.089h}\)), or Choice C (\(\mathrm{8.9h}\)) respectively.

The Bottom Line:

This problem tests a fundamental skill that appears simple but requires precise execution. The key insight is remembering that converting a percentage to a decimal always means dividing by 100, so \(\mathrm{89\%}\) becomes \(\mathrm{0.89}\).