Question
Isosceles triangle \( A B C \) has a perimeter of 96 centimeters. The base of the triangle is \( \overline{A C} \) and measures 24 centimeters. What is the measure of \( \overline{A B} \) ? 12 cm 36 cm 48 cm 72 cm
Ask by Montgomery Santiago. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The measure of \( \overline{A B} \) is 36 cm.
Solution
To determine the measure of \( \overline{A B} \) in the isosceles triangle \( A B C \):
1. **Given:**
- Perimeter of triangle \( A B C \) is 96 cm.
- Base \( \overline{A C} \) is 24 cm.
- Since the triangle is isosceles with \( A B = B C \), let \( A B = B C = x \).
2. **Set up the equation for the perimeter:**
\[
A B + B C + A C = 96 \quad \Rightarrow \quad x + x + 24 = 96
\]
\[
2x + 24 = 96
\]
3. **Solve for \( x \):**
\[
2x = 96 - 24
\]
\[
2x = 72
\]
\[
x = 36
\]
Therefore, the measure of \( \overline{A B} \) is **36 cm**.
**Answer:** 36 cm
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the measure of \( \overline{A B} \) in isosceles triangle \( A B C \), we know that the perimeter is the sum of all sides. Since the perimeter is 96 cm and the base \( \overline{A C} \) measures 24 cm, we can set up the equation: \[ \text{Perimeter} = \overline{A B} + \overline{A B} + \overline{A C} \] Let \( \overline{A B} = x \). Therefore, \[ 96 = x + x + 24 \] \[ 96 = 2x + 24 \] \[ 96 - 24 = 2x \] \[ 72 = 2x \] \[ x = \frac{72}{2} = 36 \] Thus, the measure of \( \overline{A B} \) is 36 cm.
