Exercise 13 Page 577

Let's analyze the given figure. Since we are given a triangle with a line that is parallel to one of its sides, we can use the Triangle Proportionality Theorem.

The lengths of the segments intercepted by the parallel line are proportional. Let's write a proportion using the expressions for the lengths of the segments. AB/BC=AE/ED Since we are given the lengths of AE and AD, we can find the length of ED.

AE+ED=AD

SubstituteII

AE= 12, AD= 27

12+ED= 27

SubEqn

LHS-12=RHS-12

ED=15

Now we can substitute all known lengths into our proportion. AB/BC=AE/ED ⇕ 8/BC=12/15 Finally, we will solve this equation for BC.

8/BC=12/15

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Solve for BC

MultEqn

LHS * BC=RHS* BC

8=12/15BC

ReduceFrac

a/b=.a /3./.b /3.

8=4/5BC

MultEqn

LHS * 5=RHS* 5

40=4BC

DivEqn

.LHS /4.=.RHS /4.

10=BC

RearrangeEqn

Rearrange equation

BC=10