IMO Practice Test — Perimeter
6 Questions • 10 min • Olympiad level
10:00
Question 1 of 6
hard
A rectangle has perimeter 48 cm. The length is twice the width. Find the length.
8 cm
12 cm
16 cm
24 cm
Explanation: Let W = width, L = 2W. P = 2(L+W) = 2(2W+W) = 6W = 48. W = 8, L = 16 cm.
Question 2 of 6
hard
A square and rectangle have same perimeter. Square side=10 cm, rectangle length=12 cm. Rectangle width = ?
6 cm
7 cm
8 cm
10 cm
Explanation: Square P = 4x10 = 40. Rectangle: 2(12+W)=40, so 12+W=20, W=8 cm.
Question 3 of 6
hard
A regular hexagon has side 5 cm. Perimeter = ?
25 cm
30 cm
35 cm
36 cm
Explanation: Regular hexagon: 6 equal sides. P = 6 x 5 = 30 cm.
Question 4 of 6
hard
A triangle has sides (x+2), (x+3), and (x+4) cm. Perimeter = 39 cm. Find x.
8
9
10
11
Explanation: (x+2)+(x+3)+(x+4) = 3x+9 = 39. 3x=30. x=10.
Question 5 of 6
hard
A shape has 4 sides: 5, 7, 5, 7 cm. What shape? Perimeter?
Square, 24 cm
Rectangle, 24 cm
Rhombus, 24 cm
Trapezoid, 24 cm
Explanation: Opposite sides equal (5,7,5,7) = rectangle. P = 5+7+5+7 = 24 cm.
Question 6 of 6
hard
A square's perimeter is 4 cm more than a rectangle (length=6, width=4 cm). Find square side.
5 cm
6 cm
7 cm
8 cm
Explanation: Rectangle P = 2(6+4) = 20 cm. Square P = 20+4 = 24 cm. Square side = 24/4 = 6 cm.