Respuesta :
The lengths of the sides of a similar triangle that has a perimeter of 45 m are 12 m , 15 m , 18 m
Further explanation
Firstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
sin ∠A = opposite / hypotenuse
cos ∠A = adjacent / hypotenuse
tan ∠A = opposite / adjacent
Let us now tackle the problem!
A similar triangle has the same angle, in other words the triangle has the same shape but different sizes.
Given:
The lengths of the sides of a triangle are 8 m, 10 m, 12 m
[tex]\texttt{Perimeter of First Triangle} = 8 + 10 + 12 = 30 \texttt{ m}[/tex]
[tex]\texttt{Perimeter of Second Triangle : Perimeter of First Triangle = 45 : 30}[/tex]
[tex]\texttt{Perimeter of Second Triangle : Perimeter of First Triangle = 3 : 2}[/tex]
Therefore , the lengths of the sides of a similar triangle will be:
[tex]s_1 = \frac{3}{2} \times 8 = 12 \texttt{ m}[/tex]
[tex]s_2 = \frac{3}{2} \times 10 = 15 \texttt{ m}[/tex]
[tex]s_3 = \frac{3}{2} \times 12 = 18 \texttt{ m}[/tex]
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Answer details
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle
The lengths of the sides of a similar triangle that has a perimeter of 45 m are [tex]\boxed{12{\text{ m}}}, \boxed{15{\text{ m}}}[/tex] and [tex]\boxed{18{\text{ m}}}.[/tex]
Further Explanation:
The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.
Explanation:
If the two triangles are similar to each other than the ratios of the corresponding sides are equal.
The ratio of the perimeter of the similar triangles is equal to the ratio of the sides.
Consider the first side of the similar triangle as [tex]x[/tex].
Consider the second side of the similar triangle as [tex]y[/tex].
Consider the third side of the similar triangle as [tex]z[/tex].
The lengths of the sides of a triangle are 8 m, 10 m and 12m.
The perimeter of the triangle can be obtained as follows,
[tex]\begin{aligned}{\text{Perimeter}} &= 8 + 10 + 12\\&= 30{\text{ m}}\\\end{aligned}[/tex]
The perimeter of the similar triangle is [tex]45{\text{ m}}.[/tex]
The ratio of the perimeter can be obtained as follows,
[tex]\begin{aligned}{\text{Ratio}} &= \frac{{45}}{{30}}\\&= 1.5\\\end{aligned}[/tex]
The lengths of side first side can be obtained as follows,
[tex]\begin{aligned}\frac{x}{8} &= 1.5\\x&= 1.5 \times 8\\x&= 12{\text{ m}}\\\end{aligned}[/tex]
The lengths of second side can be obtained as follows,
[tex]\begin{aligned}\frac{y}{{10}} &= 1.5\\ y&= 1.5 \times 10\\y&= 15{\text{ m}}\\\end{aligned}[/tex]
The lengths of first side can be obtained as follows,
[tex]\begin{aligned}\dfrac{z}{{12}} &= 1.5\\z&= 1.5 \times 12\\z&= 18{\text{ m}}\\\end{aligned}[/tex]
The lengths of the sides of a similar triangle that has a perimeter of 45 m are [tex]\boxed{12{\text{ m}}}, \boxed{15{\text{ m}}}[/tex] and [tex]\boxed{18{\text{ m}}}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Triangle
Keywords: angles, triangle, similar, perimeter, lengths of sides, sides, lengths, similar triangle, two right triangles, one smaller, right angles, straight angle, two acute angles, overlapping.
