Question

name: _____________________ date: _____________

1. the perimeter of an isosceles triangle is 20 cm.

a) build a table of values to show a pattern between the length of
the two equal sides and values of x between 1 cm and 5 cm.

b) describe the pattern using words.

c) write a formula to define the relationship in part b).

d) what is the length of the two equal sides for x = 9?

Explanation:

Step1: Recall the formula from part c

The formula relating \( e \) (length of equal sides) and \( x \) (length of the base) is \( e = 0.5x + 10 \)? Wait, no, let's re - derive it. The perimeter of an isosceles triangle is \( P=2e + x \), and \( P = 20 \). So \( 2e+x=20 \), then \( 2e=20 - x \), and \( e=\frac{20 - x}{2}=10-\frac{x}{2}=10 - 0.5x \).

Step2: Substitute \( x = 9 \) into the formula

Substitute \( x = 9 \) into \( e=10 - 0.5x \).
\( e=10-0.5\times9 \)
First, calculate \( 0.5\times9 = 4.5 \)
Then, \( e=10 - 4.5=5.5 \)

Answer:

The length of the two equal sides when \( x = 9 \) is \( 5.5 \) cm.