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3 years ago

11

M and N are equilateral triangles. The scale factor of M to N is 8 : 4.1 and the area of triangle M is 320 square inche. find th

e area of triangle N

2 answers:

Lesechka [4]3 years ago

7 0

Answer:

84.05 square inches

Step-by-step explanation:

Given;

Area of N = 320×(4.1/8)^2 = 84.05 square inches

Sunny_sXe [5.5K]3 years ago

3 0

Answer:

84.05 square inches

Step-by-step explanation:

Given;

Area of M = 320 square inches

Scale factor of M to N = 8 : 4.1

Since M and N are equilateral, it means all 3 sides in triangle M are equal and all 3 sides in triangle N are equal

To find the area of triangle N, we have:

$N = 320 * (\frac{4.1}{8})^2$

= 84.05 square inches

Therefore area of triangle N =

84.05 square inches

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Maurinko [17]

<h2>=>> <u>Solution (part A</u>) :</h2>

Given :

▪︎Triangle AMG is an isosceles triangle.

▪︎Measure of segment AM = (x+1.4) inches

▪︎Measure of segment MG = (2x+0.1) inches

▪︎Measure of segment AG = (3x-0.4) inches

▪︎segment AG is the base of triangle AMG.

Since AG is the base of the isosceles triangle AMG, segment AM and segment MG will be equal.

Which means :

$= \tt x + 1.4 = 2x + 0.1$

$= \tt x + 1.4 - 0.1 = 2x$

$= \tt \: x + 1.3 = 2x$

$= \tt 1.3 = 2x - x$

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Thus, the value of x = 1.3

Therefore :

▪︎The value of x = 1.3

<h2>=>> <u>Solution (Part B)</u> :</h2>

We know that :

▪︎The value of x = 1.3

Which means :

The length of the leg AM :

$= \tt x + 1.4$

$= \tt 1.3 + 1.4$

$\color{plum} \tt leg \: AM= 2.7 \: inches$

Thus, the length of the leg AM = 2.7 inches

The length of leg MG :

$= \tt 2x + 0.1$

$= \tt2 \times 1.3 + 0.1$

$= \tt 2.6 + 0.1$

$\color{plum} \tt\: leg \:MG = 2.7 \: inches$

Thus, the length of the leg MG = 2.7 inches

Since the measure of the two legs are equal (2.7=2.7), we can conclude that we have found out the correct length of each leg.

Therefore :

▪︎Measure of leg AM = 2.7 inches

▪︎Measure of leg MG = 2.7 inches

<h2>=>> <u>Solution </u><u>(</u><u>part C</u><u>)</u> :</h2>

We know that :

Value of x = 1.3

Then, measure of the base AG :

$= \tt 3x - 0.4$

$= \tt 3 \times 1.3 - 0.4$

$= \tt 3.9 - 0.4$

$\color{plum}\tt \: Base \: AG = 3.5 \: inches$

Thus, the measure of the base = 3.5 inches

Therefore :

▪︎ the length of base AG = 3.5 inches.

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frosja888 [35]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Read 2 more answers

Determine the next step for solving the quadratic equation by completing the square.

Studentka2010 [4]

Answer:

The solutions are $x=\frac{1+\sqrt{7}}{2}$ and $x=\frac{1-\sqrt{7}}{2}$

Step-by-step explanation:

we have

$0=-2x^{2}+2x+3$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$-3=-2x^{2}+2x$

Factor the leading coefficient

$-3=-2(x^{2}-x)$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$-3-0.5=-2(x^{2}-x+0.5^{2})$

$-3.5=-2(x^{2}-x+0.5^{2})$

Rewrite as perfect squares

$-3.5=-2(x-0.5)^{2}$

$7/4=(x-0.5)^{2}$

square root both sides

$x-0.5=(+/-)\sqrt{\frac{7}{4}}$

$x-\frac{1}{2}=(+/-)\frac{\sqrt{7}}{2}$

$x=\frac{1}{2}(+/-)\frac{\sqrt{7}}{2}$

$x=\frac{1+\sqrt{7}}{2}$

$x=\frac{1-\sqrt{7}}{2}$

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3 years ago