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kogti [31]
3 years ago
9

Travis is making a pattern with triangle tiles. Each side of a triangle is 3 inches long. What is the perimeter when the pattern

has 36 triangles?
Mathematics
1 answer:
Sidana [21]3 years ago
8 0

Answer:

108

Step-by-step explanation:

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The length of a rectangle is 3 m more than twice the width, and the area of the rectangle is 54 mº. Find the dimensions of the r
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Answer:

  • The dimensions of rectangle are 12 m and 4.5 m

Step-by-step explanation:

Given that, The length of a rectangle is 3 m more than twice the width, and the area of the rectangle is 54 m²

Let's assume width of rectangle be x m and length be 3 + 2x m respectively. To find the dimensions of the rectangle we will use the formula of Perimeter of rectangle

\\  { \underline{ \boxed{ \pmb{ \sf{ \purple{Area _{(rectangle)} = Length  × width}}}}}} \\ \\

Substituting values in above formula:

\\ \dashrightarrow \sf \: \:  (3 + 2x)(x)  = 54  \\

\dashrightarrow \sf \: \: 3x +  2x^2 = 54 \\

\dashrightarrow \sf \: \: - 54 + 3x + 2x^2 = 0 \\

\dashrightarrow \sf \: \: 2x^2 + 3x - 54 = 0\\

\dashrightarrow \sf \: \: 2x^2 + 12x - 9x - 54 = 0\:

\dashrightarrow \sf \: \: 2x(x + 6)  -9(x + 6) = 0\\

\dashrightarrow \sf \: \: (2x -9)(x+6) = 0  \\

\sf{x=}{\sf{\dfrac{9}{2}}}{\sf{\: or\: -6}}

\dashrightarrow  \:  \: { \underline{ \boxed{ \pmb{ \sf{\purple{ x = 4.5 }}}}}}

Hence,

  • Length of rectangle = 3 + 2x = 3 + 2(4.5) = 12 m
  • Width of the rectangle = x = 4.5m

\\ { \underline{  \pmb{ \frak{ \therefore Length \:  and \:  width  \: of  \: the  \: rectangle  \: is \:12 \: m \: and \:  4.5 \: m}}}} \\

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