All categories

3 years ago

The lengths of the

Mathematics

1 answer:

Dmitrij [34]3 years ago

4 0

Answer:

$S_{\Delta ABC}$ = 4· $S_{\Delta EDC}$

Step-by-step explanation:

From the midpoint theorem, which states that the line that a line drawn such that it joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and is equal to half the length of the third side

Therefore, the lengths of the sides of ΔDEF, drawn by joining the midpoints of ΔABC is equal to half the length of and parallel to the corresponding side of ΔABC

We therefore, have that the corresponding sides of ΔABC and ΔDEF have a common ratio and a pair of sides in each triangle form same angles, therefore;

ΔDEF is similar to ΔABC by Side, Side, Side SSS similarity.

The length of the perimeter of ΔABC, $S_{\Delta ABC}$ = 2 × The length of the perimeter of triangle ΔEDC, $S_{\Delta EDC}$

$S_{\Delta ABC}$ = 2 × $S_{\Delta EDC}$

∴ $S_{\Delta ABC}$ ≠ 4 × $S_{\Delta EDC}$

The statement which is incorrect is therefore;

$S_{\Delta ABC}$ = 4 × $S_{\Delta EDC}$ .

You might be interested in

Will give brainliest<br><br>gimme some good songs

dangina [55]

1 People, I've been sad Christine and the Queens 4:20

2 WAP (feat. Megan Thee Stallion) Cardi B, Megan Thee Stallion 3:07

3 Yo Perreo Sola - Remix Bad Bunny, Nesi, Ivy Queen 2:54

4 LITTLE NOKIA Bree Runway 2:19

5 Good News Mac Miller 5:42

Step-by-step explanation:

5 0

3 years ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

3 years ago

9. If the area of a square is given by the polynomial 4x2 – 36x + 81, then which of the

AnnyKZ [126]

Answer:

If the area of a square is given by the polynomial 4x2 – 36x + 81, then which of the

following expressions represents the length of one side of the square?

A 2x -9

2x + 9

C 4x - 18

D 4x + 18

Step-by-step explanation:

answer 4x+18

3 0

3 years ago

What is the slope of the line?

vladimir1956 [14]

Answer:

Step-by-step explanation:

exponential growth

5 0

3 years ago

7x+5+ 54 how you do this

KonstantinChe [14]

Answer:

7x+59

Step-by-step explanation:

Add 5 and 54

3 0

3 years ago

Read 2 more answers