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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

7. Scale Drawings and Models

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Exercise 27 Page 605

BD is the median of AC.

D

Practice makes perfect

We want to find the value of AC in the given diagram.

We are given that AD=3x+5 and CD=5x-1. Also, we know that BD is the median of AC. AD=DC ⇒ 3x+5=5x-1 Let's solve the above equation for x.

3x+5=5x-1

▼

Solve for x

LHS-5x=RHS-5x

- 2x+5=- 1

LHS-5=RHS-5

- 2x=- 6

.LHS /- 2.=.RHS /- 2.

x=3

Knowing the value of x, we can find the length of one of the segments of AC. Let's find AD.

AD=3x+5

x= 3

AD=3( 3)+5

▼

Evaluate

Multiply

AD = 9 + 5

Add terms

AD=14

Since BD is the median of AC, to find the length of AC we need to multiply the length of AD by 2. AC = AD * 2 ⇒ AC = 28 We see that the answer is D.

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Exercises p.602-605