In a rhombus whose side measures 20 and the smaller angle is 38°. Find the length of the larger diagonal, to the nearest tenth.
1 answer:
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Answer:
option D. 126 cm
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
Triangles PQR and XYZ are similar by AA Similarity Theorem
so
Let
z ---> the scale factor
substitute the given values
step 2
Find the perimeter of triangle XYZ
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z ----> the scale factor
p_1 ----> the perimeter of triangle XYZ
p_2 ---> the perimeter of triangle PQR
so
The perimeter of triangle PQR is
we have
substitute
therefore
The perimeter of triangle XYZ is 126 cm
