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Two triangles are similar . The sides of the smaller triangle have lengths of 8,12, and 16 centimeters. The perimeter of the larger triangle is 54 centimeters. Find the length of the shortest side of the triangle.

Respuesta :

calculista

Answer:

The shortest side of the larger triangle is 12 cm

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its perimeters is equal to the scale factor

step 1

Find the perimeter of the smaller triangle

[tex]P=8+12+16=36\ cm[/tex]

step 2

Find the scale factor

Divide the perimeter of the larger triangle by the perimeter of the smaller triangle

so

[tex]\frac{54}{36}= 1.5[/tex]

step 3

Find the length of the shortest side of the larger triangle

Multiply the shortest side of the smaller triangle by the scale factor

so

[tex](8)1.5=12\ cm[/tex]

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