A square has each side of length 2 units. A triangle is drawn inside the…
2024
A square has each side of length 2 units. A triangle is drawn inside the square with its base along one full side of the square (length 2 units) and its apex at the midpoint of the opposite side, so that the height of the triangle is also 2 units. Find the ratio of the area of the square to the area of the triangle.
- A.
1:2
- B.
2:1
- C.
2:3
- D.
3:2
Show answer & explanation
Correct answer: B
The area of a square with side s is s2, and the area of a triangle with base b and height h is ½ × b × h. To compare two shapes' areas, compute each area from the given dimensions independently, then form the ratio in the order the question asks for.
From the figure, the square's side is 2 units, so its area = 22 = 4.
The triangle shares the square's side as both its base and height (base = height = 2), so its area = ½ × 2 × 2 = 2.
The ratio of the square's area to the triangle's area is 4 : 2, which simplifies to 2 : 1.
As a check: whenever a triangle's base and height both equal a square's side length, its area is always exactly half the square's area (½ × s × s = s2/2). Here that gives 4/2 = 2, confirming the triangle's area and the 2:1 ratio independently of the step-by-step calculation above.
