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This isosceles triangle has two sides of equal length, [tex]a[/tex], that are longer than the length of the base, [tex]b[/tex]. The perimeter of the triangle is 15.7 centimeters. The equation [tex]2a + b = 15.7[/tex] models this information.

If one of the longer sides is equal to [tex]x[/tex], what equation can be used to find [tex]x[/tex]?



Answer :

GinnyAnswer
To solve for the length of the base [tex]\( b \)[/tex] of an isosceles triangle given that its perimeter is 15.7 centimeters and the lengths of the two equal sides are [tex]\( a \)[/tex], we follow these steps:

1. Understand the given information and the equation:
- The perimeter of an isosceles triangle is given as 15.7 cm.
- The lengths of the two equal sides are represented by [tex]\( a \)[/tex].
- The length of the base is represented by [tex]\( b \)[/tex].
- The equation modeling the perimeter of the triangle is:
[tex]\[ 2a + b = 15.7 \][/tex]

2. Rearrange the equation to solve for [tex]\( b \)[/tex]:
- Begin with the given equation:
[tex]\[ 2a + b = 15.7 \][/tex]
- Subtract [tex]\( 2a \)[/tex] from both sides of the equation to isolate [tex]\( b \)[/tex]:
[tex]\[ b = 15.7 - 2a \][/tex]

3. Conclusion:
- The length of the base [tex]\( b \)[/tex] in terms of the length of the sides [tex]\( a \)[/tex] is:
[tex]\[ b = 15.7 - 2a \][/tex]

This equation tells us how to find the length of the base if we know the length of the two equal sides of the isosceles triangle.

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