a Create a ratio for the original triangle of the height to the base. Then, use the similarity of the triangles to write a proportion.
B
b The scale factor tells you how many times larger the enlarged triangle is.
A
a 32.5 centimeters
B
b 1:2.5
Practice makes perfect
a To begin, we will create a ratio that relates the given base and height of the original triangle.
Height/Base ⇒ 7 cm/13 cmIt is given that the height of the enlarged triangle measures 17.5 centimeters. If we let x represent the base of the enlarged triangle, we can create the following proportion.
7/13 = 17.5/x
By solving for x, we can determine the base of the enlarged triangle.
The base of the enlarged triangle will be 32.5 centimeters.
b The scale factor tells us by how many times the triangle has been enlarged. By dividing two of the corresponding sides in the triangles, we can determine the scale factor. Any pair of corresponding sides will do.
Using the base:& 17.5/7 = 2.5 [0.8em]
Using the height:& 32.5/13= 2.5
The scale factor is 2.5. We can write as 1:2.5, where 1 represents a side of the smaller triangle, and 2.5 represents a side of the larger triangle.
