A triangle drawn on a map has sides of lengths 7.0 cm, 11 cm, and 15 cm. The shortest of the corresponding real-life distances is 94 km.The longest of the real-life distances is _____ kilometers.

Question

mathstudent55 · Answer

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The two triangles are similar, so the lengths of corresonding sides are in the same ratio.

mathstudent55 · Answer

Since we know the shortest scale side (7.0 cm) corresponds to a real 94 km, we can establish a ratio between the scale drawing and the real measurements. Then we let it be equal to the ratio of the largest scale side (15 cm) to the unknown largest real side.

We get this proportion:

$ \dfrac{7.0~cm}{94 ~km} = \dfrac{15 ~cm}{x} $

Cross multiply and solve for x.

anonymous · Answer

i keep gettin a long decimal and doesnt seem right

mathstudent55 · Answer

$7x = 15 \times 94 $

$7x = 1410$

$\dfrac{7x}{7} = \dfrac{1410}{7} $

$ x = 201.42857... $

Answer: approximately 201.4 km