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You leave your house to go the mall. You drive due north 8 miles, due east 7.5 miles, and due north again 2 miles. Answer b and c.

You leave your house to go the mall. You drive due north 8 miles, due east 7.5 miles-example-1
User Zanderle
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Answer:

  • CD = 1.5 miles
  • AE = 12.5 miles

Explanation:

Given the figure with triangle ABC similar to triangle EDC and AB=8 mi, ED=2 mi, BD = 7.5 mi, you want the measures of CD and AE.

b. CD

Similar triangles will have corresponding sides proportional. That means ...

ED/CD = AB/CB

2/CD = 8/(7.5 -CD)

Inverting the ratios and multiplying by 8 gives ...

4·CD = 7.5 -CD

5·CD = 7.5 . . . . . . . add CD

CD = 1.5 . . . . . . . . . divide by 5

c. AE

The distance AE is the hypotenuse of a right triangle with side lengths 7.5 and (8+2) = 10. The Pythagorean theorem can be used to find AE:

AE² = 7.5² +10² = 56.25 +100 = 156.25

AE = √156.25 = 12.5

AE = 12.5 miles, the distance to the mall.

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Additional comment

You may recognize these triangles are 3-4-5 triangles. ABC has a scale factor of 2, so has side lengths 6-8-10. EDC has a scale factor of 1/2, so has side lengths 1.5, 2, 2.5. The triangle with AE as its hypotenuse is the sum of these, so has a scale factor of 2.5 (miles).

AE = (2.5 miles) · 5 = 12.5 miles

User Manzhikov
by
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