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Morgarella [4.7K]
4 years ago
15

1. The length of a rectangle is 3 in. more than the width. The perimeter of the rectangle is 24 in.

Mathematics
1 answer:
Westkost [7]4 years ago
4 0

Answer:

Let the width be x

Length = x + 3

Perimeter = 2(l+b)

24 = 2(x+3+x)

12 = 2x + 3

2x = 9

x = 4.5

Width = 4.5 in

Length = 4.5+3 = 7.5 in.

Hope this helps!

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Step-by-step explanation:

60/4 = 15

60 x 15 = 900

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Write an equation of the perpendicular bisector of the segment with endpoints Q(−2,0)
olga nikolaevna [1]

The equation of perpendicular bisector of QR is:

y = -\frac{2}{3}x+\frac{22}{3}

Step-by-step explanation:

Given points are:

Q(-2,0)\ and\ R(6,12)

First of all, we have to find the slope of the given line

So,

m = \frac{y_2-y_1}{x_2-x_1}

Here

(x1,y1) = (-2,0)

(x2,y2) = (6,12)

Let m1 be the slope of QR:

Then

m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of two perpendicular lines is -1

m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}

The bisector will pass through the mid-point of QR

M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\M = (\frac{-2+6}{2}, \frac{0+12}{2})\\M = (\frac{4}{2}, \frac{12}{2})\\M = (2,6)

Slope-intercept form of equation is:

y = m_2x+b

Putting the value of slope

y = -\frac{2}{3}x+b

Putting (2,6) in the equation

6 = -\frac{2}{3}(2)+b\\6 = -\frac{4}{3}+b\\b = 6+\frac{4}{3}\\b = \frac{18+4}{3}\\b = \frac{22}{3}

So,

y = -\frac{2}{3}x+\frac{22}{3}

Hence,

The equation of perpendicular bisector of QR is:

y = -\frac{2}{3}x+\frac{22}{3}

Keywords: Mid-point, equation of line

Learn more about equation of line at:

  • brainly.com/question/774670
  • brainly.com/question/763150

#LearnwithBrainly

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Step-by-step explanation:

130 because the angle is obviously obtuse

50 is acute

130 is obtuse

130 is your answer.

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