Five congruent small rectangles are joined, as shown, to form one large rectangle. The large rectangle is mathematically similar to each of the small rectangles. For each small rectangle, find the ratio length of the shorter side : length of the longer side

Answer:

12) A

Let length (longer side) of large rectangle = L Let width (shorter side) of large rectangle = W
Let length (longer side) of small rectangle = | Let width (shorter side) of small rectangle = w
From the diagram, we can see that:
L = 5w
W = I
We wish to work out the ratio ‘w: I’
We know that the small rectangle is congruent to the large rectangle. Therefore, the ratio of their sides should also be the same. That is, L/W =l/w

We know that L = 5w and W = I

5w/l =l/w

5w² = l²
√5w = l

5w/l =1/√5

So ratio of width: length = 1:√5