The perimeter of the rectangle shown below is 16a+2b. Which expression represents the length of the rectangle?
A. 3a+2b C. 2a-3b
B.10a+2b D.6a+4b
The scale factor of two similar polygon is 4:5. The perimeter of the larger polygon is 200 inches. What is the perimeter of the smaller polygon?
F.250 inches H.80 inches
G.160 inches J.40 inches
For the first question, we are given that the perimeter of the rectangle is 16a+2b. The perimeter of a rectangle is given by the formula: 2(length + width). To find the expression for the length, we need to solve the equation: 2(length + width) = 16a+2b.
Let's break down the given options to find which one represents the length of the rectangle.
A. 3a+2b: This represents the sum of the length and the width, not just the length.
B. 10a+2b: This represents the sum of the length and the width, not just the length.
C. 2a-3b: This represents the sum of the length and the width, not just the length.
D. 6a+4b: This represents the sum of the length and the width, not just the length.
None of the given options represents the length of the rectangle. Given the information provided, the expression for the length is not available.
For the second question, we are given that the scale factor of two similar polygons is 4:5. We are also given that the perimeter of the larger polygon is 200 inches. We need to find the perimeter of the smaller polygon.
Let's set up a proportion to solve for the perimeter of the smaller polygon:
(Perimeter of larger polygon)/(Perimeter of smaller polygon) = (Scale factor of larger polygon)/(Scale factor of smaller polygon)
Plugging in the given values:
200/Perimeter of smaller polygon = 5/4
To solve for the perimeter of the smaller polygon, we can cross-multiply:
200 * 4 = (Perimeter of smaller polygon) * 5
800 = (Perimeter of smaller polygon) * 5
Now, we can solve for the perimeter of the smaller polygon:
(Perimeter of smaller polygon) = 800/5 = 160
Therefore, the perimeter of the smaller polygon is 160 inches. The correct option is G. 160 inches.