I only need help on the estimate problems

In the figure, the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD is . The area of polygon ABCDE is s

Gekata [30.6K]

Step 1

Find the perimeter of rectangle ABDE

we know that

the perimeter of rectangle is equal to

$P=2b+2h$

In this problem

$b=ED=2\ units$

$h=AE=6\ units$

substitute

$P=2*2+2*6=16\ units$

Step 2

Find the perimeter of triangle BCD

we know that

the perimeter of triangle is equal to

$P=BD+DC+BC$

In this problem we have

$BD=AE=6\ units$

$DC=BC$

Applying the Pythagoras theorem

$DC^{2}=4^{2}+3^{2}$

$DC^{2}=25$

$DC=5\ units$

substitute

$P=6+5+5=16\ units$

Find the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD

we have

the perimeter of rectangle is equal to

$P=16\ units$

the perimeter of the triangle is

$P=16\ units$

so

the ratio is equal to

$\frac{16}{16} =1$

therefore

<u>the answer Part 1) is the option B</u>

$1$

Step 3

Find the area of polygon ABCDE

we know that

The area of polygon is equal to the sum of the area of rectangle plus the area of triangle

Area of rectangle is equal to

$A=AE*BD=6*2=12\ units^{2}$

Area of the triangle is equal to

$A=\frac{1}{2}AEh$

the height h of the triangle is equal to $4\ units$

substitute

$A=\frac{1}{2}(6)(4)=12\ units^{2}$

The area of polygon is

$12\ units^{2}+12\ units^{2}=24\ units^{2}$

therefore

<u>the answer part 2) is the option C</u>

$24\ units^{2}$

7 0

4 years ago

Read 2 more answers

The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and

morpeh [17]

Answer:

k = 63

Step-by-step explanation:

Given: k's factors are 1, 3, 7, ___, ___, and k.

(1) $3^{2}$ is a factor of k.

This implies that there are two factors of 3 i..e, 9 is also a factor of k.

Also, $3\times 7=21$ is a factor of k.

Therefore, k's factors are 1, 3, 7, 9, 21, and k.

As there are two 3's and a 7 in factors of k, then is also a factor.

(2) $7^{2}$ is not a factor of K.

If $7^2$ is not a factor of k and total number of factors is 6, there must be two factors of 3 ('K' has exactly two positive prime factors) as otherwise, if we use a non-prime factor, then k would have more than 6 factors.

So, K's factors are 1, 3, 7, 9, 21, 63.

7 0

4 years ago

-4x + (-3) =x +3 What is X equivalent to

stiks02 [169]

Answer: x= −6 /5 is the answer

4 0

3 years ago

Read 2 more answers

When the british system of units was first developed, what was the most common object used as a basis for measuring length?

mezya [45]

I believe its the human body

6 0

4 years ago

If you create a box-and-whisker plot for the data set, which expression correctly calculates the third quartile, Q3, of the data

dangina [55]

Answer:

D)

(4.4+4.8)

2

Step-by-step explanation:

there is no step by step explanation

8 0

3 years ago