Question

practice d: (first taught in lesson 29) △stu is isosceles and the length of base overline{su} is 9. find the other two side lengths if st = 4y - 3 and tu = 2y + 5. after you enter your answer press go. st = tu =

Explanation:

Step1: Set up equation for isosceles triangle

In an isosceles triangle \( \triangle STU \) with base \( SU \), the two equal sides are \( ST \) and \( TU \). So, \( ST = TU \).
\( 4y - 3=2y + 5 \)

Step2: Solve for \( y \)

Subtract \( 2y \) from both sides:
\( 4y-2y - 3=2y-2y + 5 \)
\( 2y-3 = 5 \)
Add 3 to both sides:
\( 2y-3 + 3=5 + 3 \)
\( 2y=8 \)
Divide both sides by 2:
\( y=\frac{8}{2}=4 \)

Step3: Find \( ST \) and \( TU \)

For \( ST = 4y - 3 \), substitute \( y = 4 \):
\( ST=4\times4 - 3=16 - 3 = 13 \)
For \( TU = 2y + 5 \), substitute \( y = 4 \):
\( TU=2\times4 + 5=8 + 5 = 13 \)

Answer:

\( ST = 13 \), \( TU = 13 \)