Ask question

Ask question

All categories

3 years ago

11

The sides of an equilateral triangle measure 16 inches. The midpoints of the sides of the triangle are joined to form another eq

uilateral triangle with sides that are half the length of the outer triangle. This process is continued until three triangles are inscribed in the first triangle. The sum of the perimeters of all four triangles is

1 answer:

Alex Ar [27]3 years ago

5 0

Answer:

90 inches

Step-by-step explanation:

The perimeter of the inscribed triangle is 1/2 that of the enclosing triangle. So, the total of perimeters is ...

(3·16 in)(1 +1/2 +1/4 +1/8) = (48 in)(15/8) = 90 inches

You might be interested in

Please help me!!! Brainliest answer!!!

Vsevolod [243]

1.

$g+h=-7+3=\boxed{-4}$

2.

$g-h=-7-3=\boxed{-10}$

3.

$h-g=3-(-7)=3+7=\boxed{10}$

4.

$gh=-7\cdot3=\boxed{-21}$

5.

$g+h^2=-7+3^2=-7+9=\boxed{2}$

6.

$g^2-h=(-7)^2-3=49-3=\boxed{46}$

5 0

3 years ago

On your paper, construct a rectangle on a coordinate plane that satisfies these criteria.

german

Answer:

$A = (5,3)$

$B = (-5,3)$

$C = (-5,-8)$

$D = (5,-8)$

Step-by-step explanation:

Required

$Perimeter = 42$

Construct a rectangle whose perimeter is 42 units and satisfies the given conditions.

First, name the rectangle ABCD.

Such that:

$A = (x_1,y_1)$

$B = (x_2,y_2)$

$C = (x_3,y_3)$

$D = (x_4,y_4)$

For the rectangle to be either horizontal or vertical, then:

$y_1 = y_2$ and $y_3 = y_4$

We have that:

$Perimeter = 42$

Replace perimeter with its formula

$2(AB + BC) = 42$

Divide both sides by 2

$AB + BC = 21$

This implies that, the distance between adjacent sides (through the edges) must be equal to 21

Having said that: a set of coordinates that satisfy the given conditions are:

$A = (5,3)$ -- First quadrant

$B = (-5,3)$ -- Second quadrant

$C = (-5,-8)$ -- Third quadrant

$D = (5,-8)$ -- Fourth quadrant

The above quadrants satisfy the condition:

$y_1 = y_2$ and $y_3 = y_4$

<u>HOW TO KNOW THE PERIMETER IS 42</u>

To do this, we simply calculate the distance between the edges and add them up

<u>Distance is calculated as:</u>

<u></u> $D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$ <u></u>

<u></u>

<u>For AB</u>

$A = (5,3)$

$B = (-5,3)$

$D_1 = \sqrt{(5 - (-5))^2 + (3 - 3)^2}= \sqrt{(10)^2 + (0)^2} = \sqrt{100} = 10$

<u>For BC</u>

$B = (-5,3)$

$C = (-5,-8)$

$D_2 = \sqrt{(-5 - (-5))^2 + (3 - (-8))^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11$

<u>For CD</u>

$C = (-5,-8)$

$D = (5,-8)$

$D_3 = \sqrt{(-5 -5)^2 + (-8 - (-8))^2}= \sqrt{(-10)^2 + (0)^2} = \sqrt{100} = 10$

<u>For DA</u>

$D = (5,-8)$

$A = (5,3)$

$D_4 = \sqrt{(5 -5)^2 + (-8 -3)^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11$

So, the perimeter is:

$P = D_1 + D_2 + D_3 + D_4$

$P = 10 + 11 + 10 +11$

$P = 42$

See attachment for rectangle

8 0

2 years ago

Henry runs 10 miles in 85 min. At the same rate how many minutes would he take to run 8 miles?

sp2606 [1]

For 10 miles, he takes = 85 min

then, 1 mile = 85/10 min.

Now, for 8 miles, it would be 85*8/10 = 68 minutes

6 0

3 years ago

What is the word form of 90.04

Pachacha [2.7K]

Answer:Ninety and 4 hundredths

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

6. A researcher conducted a study to investigate the relationship between the price of a

tensa zangetsu [6.8K]

I would have to say E because none of those are the answer

8 0

2 years ago