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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Equilateral and Isosceles Triangles

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Exercise 31 Page 613

There are three possible cases.

$t = 6$
$t = 8$
$t = 10$
Explanation: See solution.

Practice makes perfect

Depending on which sides are assigned what expression, we have three possible cases.

By equating the expressions for the leg lengths in the three cases, we can solve for the value of $t$ that makes the triangle's legs congruent.

Case	Equation	Solve for $t$
First	$5 t - 12 = t + 20$	$t = 8$
Second	$5 t - 12 = 3 t$	$t = 6$
Third	$3 t = t + 20$	$t = 10$

Having solved for

t

in each of the equations, we can figure out the length of the legs.

\underline{First Case : t = 8} 5 t - 12 : 5 (8) - 12 = 28 t + 20 : 8 + 20 = 28 3 t : 3 (8) = 24 \underline{Second Case : t = 6} 5 t - 12 : 5 (6) - 12 = 18 t + 20 : 6 + 20 = 26 3 t : 3 (6) = 18 \underline{Third Case : t = 10} 5 t - 12 : 5 (10) - 12 = 38 t + 20 : 10 + 20 = 30 3 t : 3 (10) = 30

Subchapter links

Communicate Your Answer p.607

Monitoring Progress p.609-611

Exercises p.612-614