A 3 by 2 rectangle is split into four congruent right-angled triangles, as shown in the left-hand diagram.
Those four triangles are rearranged to form a rhombus, as shown in the right-hand diagram.
What is the ratio of the perimeter of the rectangle to the perimeter of the rhombus?
A. 3 : 2
B. 2 : 1
C. 1 : 1
D. 1 : 2
E. 2 : 3
C. 1 : 1
First note that the perimeter of the rectangle is 2(2 + 3) = 10.
The diagram shows one of the four congruent triangles into which the rectangle is divided.
By Pythagoras’ Theorem, l2 = 22 + 1.52 = 4 + 2.25 = 6.25.
Therefore l =√6.25 = 2.5. So the perimeter of the rhombus is 4 × 2.5 = 10.
Hence the ratio of the two perimeters is 10 : 10 = 1 : 1.
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