The areas of two similar triangles are 25 cm2 and 36 cm2 respectively. If the perimeter of the second triangle is 24 cm, find the corresponding perimeter of the first triangle.

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]

johanrusli johanrusli · Answer 2 · 2025-04-26T16:40:47-04:00

The corresponding perimeter of the first triangle is 20 cm

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.

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]

Conclusion:

The corresponding perimeter of the first triangle is 20 cm

[tex]\texttt{ }[/tex]

Learn more

Calculate Angle in Triangle : https://brainly.com/question/12438587
Periodic Functions and Trigonometry : https://brainly.com/question/9718382
Trigonometry Formula : https://brainly.com/question/12668178

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle