Answer:
The corresponding perimeter of the first triangle is 20 cm
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor and the ratio of its areas is equal to the scale factor squared
step 1
Find the scale factor
Let
z -----> the scale factor
x ----> area of the second triangle
y ---> area of the first triangle
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=36\ cm^2\\y=25\ cm^2[/tex]
substitute
[tex]z^{2}=\frac{36}{25}[/tex]
[tex]z=\frac{6}{5}[/tex]
step 2
Find the perimeter of the first triangle
Let
z -----> the scale factor
x ----> perimeter of the second triangle
y ---> perimeter of the first triangle
so
[tex]z=\frac{x}{y}[/tex]
we have
[tex]z=\frac{6}{5}[/tex]
[tex]x=24\ cm[/tex]
substitute the values and solve for y
[tex]\frac{6}{5}=\frac{24}{y}[/tex]
[tex]y=24(5)/6\\y=20\ cm[/tex]
The corresponding perimeter of the first triangle is 20 cm
Firstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
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.
We could calculate the perimeter of the first triangle by following formula:
[tex]\texttt{Area First Triangle} : \texttt{Area Second Triangle} = (\texttt{Perimeter First Triangle})^2 : (\texttt{Perimeter Second Triangle})^2[/tex]
[tex]25 : 36 = (\texttt{Perimeter First Triangle})^2 : 24^2[/tex]
[tex]\sqrt{25} : \sqrt{36} = \texttt{Perimeter First Triangle} : 24[/tex]
[tex]5 : 6 = \texttt{Perimeter First Triangle} : 24[/tex]
[tex]\texttt{Perimeter First Triangle} = \frac{5}{6} \times 24[/tex]
[tex]\texttt{Perimeter First Triangle} = 20 \texttt{ cm}[/tex]
[tex]\texttt{ }[/tex]
The corresponding perimeter of the first triangle is 20 cm
[tex]\texttt{ }[/tex]
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle
