Find the length and perimeter of a rectangle if its width is 19 m and its area is 475 m?.

Mathematics

1 answer:

Allisa [31]2 years ago

4 0

The length of the rectangle is: 25 m

The perimeter of the rectangle is: 88 m

<h3>What is the Area and Perimeter of a Rectangle?</h3>

Area of a rectangle = (length)(width).

Perimeter of a rectangle = 2(length + width).

Give the following:

Width of rectangle = 19 m

Area of rectangle = 475 m²

Find the Length using the area formula:

475 = (length)(19)

475/19 = length

Length of the rectangle = 25 m

Find the perimeter of the rectangle

Perimeter of the rectangle = 2(25 + 19)

Perimeter of the rectangle = 2(44)

Perimeter of the rectangle = 88 m

Thus, the length of the rectangle is: 25 m

The perimeter of the rectangle is: 88 m

Learn more about the area and perimeter of rectangle on:

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Consider rolling two fair dice one 3-sided the other 5-sided

Ne4ueva [31]

Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose

$1\leq x\leq 3,\quad 1\leq y \leq 5$

We have $P(X=x)=\frac{1}{3}$ and $P(Y=y)=\frac{1}{5}$ , because the dice are fair.

Now we use the assumption of independence to claim that

$P(X=x, Y=y) = P(X=x)\cdot P(Y=y) =\dfrac{1}{3}\cdot\dfrac{1}{5} = \dfrac{1}{15}$

Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:

2 in a unique way (1+1)
3 in two possible ways (1+2, 2+1)
4 in three possible ways
5 in three possible ways
6 in three possible ways
7 in two possible ways
8 in a unique way

This implies that the probabilities of the outcomes of $W=X+Y$ are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5