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2 years ago

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Triangle ABC is equilateral with sides 10 cm long. Triangle DEF is formed by drawing lines parallel to, and 1 cm away from, the

sides of triangle ABC as illustrated. Find the perimeter of triangle DEF.

1 answer:

Brrunno [24]2 years ago

8 0

The perimeter of equilateral triangle DEF is 24 cm.

<h3>Triangle</h3>

A triangle is a polygon with three sides and three angles. Types of triangles are<em> equilateral, isosceles, obtuse, scalene</em>.

Given that triangle ABC is equilateral, also triangle DEF is equilateral.

DE = DF = EF = 10 - 1 - 1 = 8 cm

Perimeter of DEF = 8 + 8 + 8 = 24 cm

The perimeter of equilateral triangle DEF is 24 cm.

Find out more on Triangle at: brainly.com/question/24382052

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

4 years ago

Please Help Quicly The equation 8x - 4y = 5 is dilated by a scale factor of 8 centered at the origin. What is the new slope and

Rzqust [24]

For new line, slope m=2 and y-intercept c=(-10)

Step-by-step explanation:

<em>Note : Figure given is for reference to understand better.</em>

<em>Where redline is for given line and blueline for new line</em>

<em />

The equation of given line 8x-4y=5 and it is dilated by a scale factor of 8 centered at the origin.

Step 1 : Find two points on given line.

When x=0, y=?

$8x-4y=5$

$8(0)-4y=5$

$y=\frac{-5}{4}$

When y=0, x=?

$8x-4y=5$

$8x-4(0)=5$

$x=\frac{5}{8}$

We get points $A(0,\frac{-5}{4}), B(\frac{5}{8},0)$

Step 2: Find distance from centered and scale it.

Now, It is said that line 8x-4y=5 dilated by a scale factor of 8 centered at the origin and point A and point B is on same.

So that point A and point B will also get dilated by a scale factor of 8 centered at the origin or distance of points from origin will be scaled by 8.

For point A:

Distance of point $A(0,\frac{-5}{4})$ from origin is $( \frac{-5}{4})$ unit in x-direction and zero $\frac{-5}{4})$ unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is $A'(0,-10)$

For point B:

Distance of point $B(\frac{5}{8},0)$ from origin is $(\frac{5}{8})$ unit in x-direction and zero unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is $B'(5,0)$

Step 3: Find Equation of new line.

Points $A'(0,-10)$ and $B'(5,0)$ make a new line

The equation of given as

$\frac{y-Y1}{x-X1} = \frac{Y2-Y1}{X2-X1}$

$\frac{y-(-10)}{x-0} = \frac{0-(-10)}{5-0}$

$\frac{y+(10)}{x} = 2$

$\frac{y+(10)}{x} = 2$

$y+10= 2x$

$y= 2x-10$

Now, Comparing with the equation of the line : y=mx + c

Where m=slope and c is the y-intercept

We get, Slope m=2 and y-intercept c=(-10)

8 0

3 years ago

A person must be at least 4 feet tall to ride an amusement park ride. Which inequality represents the height, h, of a person who

Nataly [62]

Answer:

4≥x

Step-by-step explanation:

The person has to be at least four feet (=) or he can be higher (>).

3 0

3 years ago

Use the distributive property and the diagram to match an expression that is equivalent to 12+4x.

Ket [755]

4(3+x)

This is because 4*3=12 and 4*x is 4x so you get 12+4x which is the original equation

8 0

3 years ago

What is the area of a rectangle whose side lengths are o and g?

Mila [183]

Answer:

Area=Base length x Height

Area= O x g.

8 0

3 years ago