The area of this figure is 100 cm^2. Its perimeter is (The figure consists of four identical squares.)

1990 AMC 8 Problem 15 — Solution

Below is the professionally curated solution for Problem 15 of the 1990 AMC 8, 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).

Difficulty rating: 930

15.

The area of this figure is $100 \text{ cm}^2.$ Its perimeter is

(The figure consists of four identical squares.)

$20 \text{ cm}$

$25 \text{ cm}$

$30 \text{ cm}$

$40 \text{ cm}$

$50 \text{ cm}$

Each of the four squares has area $\dfrac{100}{4} = 25 \text{ cm}^2$ , so each side is $5 \text{ cm}.$

The outline of this staircase shape is made up of $10$ such sides, so the perimeter is $10 \cdot 5 = 50 \text{ cm}.$

Thus, the correct answer is E .