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-BARSIC- [3]
4 years ago
12

The slopes of perpendicular line segments are three/ four fraction and d/two What is the value of d?

Mathematics
1 answer:
Anvisha [2.4K]4 years ago
5 0
Slopes of perpendicular lines are NEGATIVE RECIPROCAL to each other
namely, if say one has a slope of a/b  then the other will have a slope of \bf slope=\cfrac{a}{{{ b}}}\qquad negative\implies  -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}

what the dickens does that mean?  

well, it means that their product is \bf \cfrac{a}{b}\cdot \cfrac{-b}{a}\implies -1

so... in this case, one has a slope of 3/4 and the other has a slope of d/2

thus   \bf \cfrac{3}{4}\cdot \cfrac{d}{2}=-1\implies \cfrac{3\cdot d}{4\cdot 2}=-1\implies \cfrac{3d}{8}=-1
\\\\\\
\textit{now we cross-multiply}
\\\\\\
3d=-8\implies d=\cfrac{-8}{3}
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Find the height of a triangle that has an area of 54 cm2 with the width 3 cm less than its height.
iren2701 [21]

The height of a triangle is 9 cm

<h3>What is Triangle?</h3>
  • A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C.
  • In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space).
  • In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.
  • All triangles are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.
  • Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

given that

let the height of the triangle be x

then the width is x-3

Area = \frac{height \times length}{2}

54 = x(x -3)

54 = x^2 -3x

x = 9

height = 9 cm

width = 6cm

Therefore, the height of a triangle is 9 cm.

To learn more about the triangle with the given link brainly.com/question/11897796

#SPJ4

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