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3 years ago

What is the length of QR?

Mathematics

1 answer:

Elena L [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Since the triangle is right with hypotenuse QR

Use Pythagoras' identity to solve for QR

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

QR² = 8² + (8 $\sqrt{3}$ )²

= 64 + 192

= 256 ( take the square root of both sides )

QR = $\sqrt{256}$ = 16

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Since angle B is not given, we have to find it ourselves. We can find the measure of angle B by subtracting both the given angle values from 180 degrees because every triangle is equal to 180 degrees.

180 - 55 - 82 = 43 | The measure of sin B = 43 degrees.

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c = 6.6607...

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The rectangle below has an area of x2 + 11x + 28 square meters and a length of 2 + 7 meters.

Troyanec [42]

<h3><u>Question:</u></h3>

The rectangle below has an Área of x^2 + 11x + 28 square meters and a length of x+7 meters. What expression represents the width of the rectangle?

<h3><u>Answer:</u></h3>

The expression representing width of rectangle is (x + 4) meters

<h3><u>Solution:</u></h3>

Given that rectangle has an area x^2 + 11x + 28 square meters and a length of x + 7 meters

To find: width of the rectangle

<em><u>The area of rectangle is given as:</u></em>

$\text {Area of rectangle }=\text { length } \times \text { width }$

Here area = x^2 + 11x + 28 square meters

length = x + 7 meters

<em><u>Substituting the values in given formula,</u></em>

$\begin{array}{l}{\text { width }=\frac{x^{2}+11 x+28}{x+7}} \\\\ {\text { width }=\frac{x^{2}+4 x+7 x+28}{x+7}} \\\\ {\text { width }=\frac{x(x+4)+7(x+4)}{x+7}} \\\\ {\text { width }=\frac{(x+4)(x+7)}{x+7}}\end{array}$

Cancelling (x + 7) on numerator and denominator,

$\text { width }=(x+4)$

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