Problem 5 · Restore a missing area · 4 points
Made by AI and not reviewed by a real person.
A 12 cm-wide, 8 cm-tall rectangle has a triangular piece cut from its bottom-left corner. The piece reaches 4 cm along the bottom and 8 cm up the left side. A vertical line divides the remaining shape into two equal areas. How far is the line from the rectangle’s original left side?
- 4 cm
- 6 cm
- 5 cm
- 8 cm
- 7 cm
Show a hint
- Imagine putting the missing corner back. How does that change the amount of rectangle on each side of the line?
- Find the missing triangle’s area and half of the remaining area. Then work out how much of the original rectangle must lie left of the line.
Show the answer and solution
Answer: E — 7 cm
The missing triangle is half of a 4 cm by 8 cm rectangle, so its area is 16 cm². The remaining area is 12 × 8 − 16 = 80 cm², and half is 40 cm². The cut must be beyond the triangle, so the original rectangle to its left has area 40 + 16 = 56 cm². At a height of 8 cm, that makes the distance 56 ÷ 8 = 7 cm. The tempting 6 cm is halfway across the original rectangle, but the missing corner makes the areas on its two sides unequal.