The perimeter of a rectangle is represented by
1 answer:
The perimeter of a rectangle is represented by 4x^2 + 5x − 2. The perimeter of a smaller rectangle is represented by x^2 + 3x + 5. Which polynomial expression BEST represents how much larger the first rectangle is than the smaller rectangle?
A) 3x^2 + 2x − 7
B) 3x^2 + 2x − 3
C) 3x^2 + 8x + 3
D) 5x^2 + 8x − 7
<h3><u>Answer:</u></h3>Option A
The polynomial expression best represents how much larger the first rectangle is than the smaller rectangle is
Perimeter of a rectangle is represented by 4x^2 + 5x − 2
Perimeter of a smaller rectangle is represented by x^2 + 3x + 5
To Find : Polynomial expression that represents how much larger the first rectangle is than the smaller rectangle.
Which means we have to find difference between perimeter of both rectangles
Subtract the equation of perimeter of smaller rectangle from equation of perimeter of a larger rectangle
Difference = perimeter of a larger rectangle - perimeter of smaller rectangle
On removing the brackets we get,
Thus option A is correct
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Answer:
The Perimeter of the Figure to the nearest tenth is 18.7 units
Step-by-step explanation:
Please note I have attached an edited version of your sketch to aid my solution. Now this question can be solved in multiple ways. Here, we shall see one of them. Looking at the original sketch, we can see that the figure is actually a combination of a Triangle (Figure 1 in my sketch) and a rectangle (Figure 2 in my sketch). So we can simply find the sides of a Triangle and the sides of a Rectangle and add them. Perimeter on Figure 1:The Perimeter of a Triangle is given by the Sum of the three sides as:
AT=a+b+c
Perimeter on Sketched Figure:The perimeter of the total figure will be two sides of the triangle and the three sides of the rectangle (as the one adjacent between Fig. 1 and 2 can not be taken into account). Thus we need to find 5 different sides and add them together. Now since the figure is on a graph paper, we can read of the size of some sides, thus the left side of the triangle is units and the base of the triangle is also units. Now to find the last unknown side we can take Pythagorian theorem, since our triangle is a Right triangle, (i.e. one angle is 90°). Pythagoras states that the squared of the hypotenuse of a right triangle is equal to the sum of the squares of the other two legs of the triangle (where the hypotenuse side is always across the 90° angle. So here we can say that: where is the hypotenuse and our unknown side. So plugging in values and solving for we have: units.
Perimeter on Figure 2:
The Perimeter of the Rectangle is given by:
Ar=2(w+l)
