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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset Vaia Explanations$ Math

Student Edition · 801 pages

ISBN: 9780078884801

Chapter 2: Q59. (page 96)

The scale factor for two similar triangles is 2:3. The perimeter of the smaller triangle is 56 cm. What is the perimeter of the larger triangle in centimeters?

Short Answer

Expert verified

The perimeter of larger triangle is $84 cm$ .

Step by step solution

01

Step 1. Perimeter of a triangle.

The basic formula to calculate the perimeter of a triangle with sides 'a', 'b', and 'c' is: $a + b + c$

02

Step 2. Use given information and determine the equation.

Let the perimeter of larger triangle be x.

Scale factor of two triangles is $2 : 3.$

Perimeter of smaller triangle $56 cm$

$\frac{2}{3} = \frac{56}{x}$

03

Step 3. Solve for x.

The equation can be written as:

$\begin{array}{l} \frac{2}{3} = \frac{56}{x} \\ 2 x = 56 \times 3 \\ 2 x = 168 \\ x = 84 cm . \end{array}$ .

Hence, the perimeter of larger triangle is $84 cm .$

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