Rectangles - Geometry

To solve, simply use the fomula for the perimeter of a square. Thus,

The perimeter of a rectangle is found by adding all the side lengths together. In a rectangle there are two widths and two lengths.

In other words, simply use the formula for the perimeter of a rectangle and let,

.

Thus,

To solve, simply use the formula for the perimeter of a rectangle. Thus,

To solve, simply use the formula for the perimeter of a rectangle. Thus,

If the formula escapes you, simply draw a picture and add all of the sides together. Rememeber, a rectangle has 4 sides, two are equal and the other 2 are equal.

To determine if the rectangles are similar, set up a proportion comparing the short sides and the long sides from each rectangle:

cross-multiply

since that's true, the rectangles are similar.

To find the scale factor, either divide 25 by 10 or 7.5 by 3. Either way you will get 2.5.

Two rectangles are similar if and only if their sides are in proportion. Specifically,

Rectangle Rectangle

if

Since is located at the point , it follows that and . Since is located at the point , it follows that and . Substituting in the aforementioned proportion statement, we get

.

Reducing to lowest terms, this is

.

This is false, so Rectangle Rectangle .

Recall how to find the area of a rectangle:

Now, plug in the given length and width to find the area.

First we must find the length of the rectangle before we can solve for the diagonal. With a length shorter than twice the width, we can solve for length by drafting an algebraic equation:

Now that we know the values for length and width, we can use the Pythagorean Theorem to solve for the diagonal:

To find the width, we must take half of the length, which means we must divide the length by 2. Then we must take 2 more than that number, which means we must add 2 to the number. Combining these, we get:

w = ½ l + 2

The width equals 3 times the length, so 3l, plus an additional two inches, so + 2, = 3l + 2

We can solve this by setting up a proportion and solving for x,the length of the shorter side of the house. If the drawing is scale and is 6 : 8, then the actual house is x : 64. Then we can cross multiply so that 384 = 8_x_. We then divide by 8 to get x = 48.

For polygons to be similar, side lengths must be in proportion.

Case 1:

and 100 in the first rectangle correspond to and 400 in the second, respectively.

The resulting proportion would be:

This is impossible since must be a positive side length.

Case 2:

and 100 in the first rectangle correspond to 400 and in the second, respectively.

The correct proportion statement must be:

Cross multiply to solve for :

200 cm is the only possible solution.

By similarity, we can set up the proportion:

Substitute:

All sides being equal is a condition for congruency, not similarity. Similarity focuses on the ratio between rectangles and not on the equivalency of all sides. As for the statement regarding the equal angles, all rectangles regardless of similarity or congruency have four 90 degree angles.

For two rectangles to be similar, their sides have to be proportional (form equal ratios). The ratio of the two longer sides should equal the ratio of the two shorter sides.

However, the left ratio in our proportion reduces.

We can then solve by cross multiplying.

We then solve by dividing.

Recall how to find the area of a rectangle:

Now, plug in the given length and width to find the area.

For two rectangles to be similar, their sides must be in the same ratio.

This problem can be solved using ratios and cross multiplication.

Let's denote the unknown width of the right rectangle as x.

The goal is to solve for the height of the second rectangle.

Similar rectangles function on proportionality - that is, the ratios of the sides between two rectangles will be the same. In order to determine the height, we will be using this concept of ratios through solving for variables from the area.

First, it's helpful to achieve full dimensions for the first rectangle.

It is given that its base length is 5, and it has an area of 20.

This means the first rectangle has the dimensions 5x4.

Now, we may utilize the concept of ratios for similarity. The side lengths of the first rectangle is 5x4, so the second recatangle must have sides that are proportional to the first's.

We have the information for the first rectangle, so the data may be substituted in.

is the ratio factor that will be used to solve for the height of the second rectangle. This may be substituted into the area formula for the second rectangle.

Therefore, the height of the second rectangle is 10.

The goal of this problem is to figure out what base length of the second rectangle will make it similar to the first rectangle.

Similar rectangles function on proportionality - that is, the ratios of the sides between two rectangles will be the same. In order to determine the base, we will be using this concept of ratios through solving for variables from the perimeter.

First, all the dimensions of the first rectangle must be calculated.

This can be accomplished through using the perimeter equation:

This means the dimensions of the first rectangle are 10x5. We will use this information for the ratios to calculate dimensions that would yield the second rectangle similar because of proprotions.

is the ratio factor we will use to solve for the base of the second rectangle.

This will require revisiting the perimeter equation for the second rectangle.

Two rectangles are similar if their length and width form the same ratio. The small tile has a width of and a width of , providing us with the following ratio:

Since the length of similar triangles is twice their respective width, the length of the large tile can be determined as such: