1990 AMC 8 Problem 15

Attempt Problem 15 of the 1990 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

15.

The area of this figure is 100 cm2.100 \text{ cm}^2. Its perimeter is
(The figure consists of four identical squares.)
20 cm20 \text{ cm}
25 cm25 \text{ cm}
30 cm30 \text{ cm}
40 cm40 \text{ cm}
50 cm50 \text{ cm}
Answer: E
Concepts:areaperimeter
Small hint:
Each of the four squares has area 1004=25 cm2\dfrac{100}{4} = 25 \text{ cm}^2
Big hint:
Find the side length of one square, then count how many side lengths make up the outline
Solution:
Each of the four squares has area 1004=25 cm2\dfrac{100}{4} = 25 \text{ cm}^2, so each side is 5 cm.5 \text{ cm}.
The outline of this staircase shape is made up of 1010 such sides, so the perimeter is 10⋅5=50 cm.10 \cdot 5 = 50 \text{ cm}.
Thus, the correct answer is E .
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