Answer: The length of the smaller rectangle rounded to the nearest tenth is 2.9 inches
Step-by-step explanation: The question states that we have two rectangles with the perimeters given as 14 inches (larger) and 10 inches (smaller) respectively.
With this bit of information given, we can derive a ratio for both rectangles which is, ratio of larger rectangle to smaller rectangle and that equals
14:10
And this is further simplified into 7:5 ( divide both sides by 2 and reduce to their simplest form)
What this simply mean is that, for every 7 units measured on the larger rectangle, the smaller rectangle measures 5 units on the corresponding side. So if for example the larger rectangle measures 7/2 units on one side, the smaller rectangle would measure 5/2 units on the corresponding side.
Having been given the length of the larger rectangle as 4 inches, we can use the ratio we derived to calculate the length of the smaller rectangle as follows;
7:5 = 4:x OR
7/5 = 4/x
By cross multiplication we now have
7(x) = 5(4)
7x = 20
Divide both sides of the equation by 7
x = 2.86
Rounded to the nearest tenth,
x = 2.9 inches
