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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 6.3 centimeters, which equation can be used to find the length of the base?

A. [tex]2(6.3) + b = 15.7[/tex]

B. [tex]6.3 + b = 15.7[/tex]

C. [tex]2a + 6.3 = 15.7[/tex]

D. [tex]2(6.3 + b) = 15.7[/tex]



Answer :

GinnyAnswer
To determine the length of the base \( b \) of the isosceles triangle, we start with the given information and the equation that models it:

1. We are given that each of the two equal sides of the isosceles triangle is \( a \), and we know \( a = 6.3 \) centimeters.
2. The perimeter of the triangle is 15.7 centimeters.
3. The equation modeling the perimeter, given \( a \), is \( 2a + b = 15.7 \).

Now we substitute the given value of \( a \) into the equation:

[tex]\[ 2 \cdot 6.3 + b = 15.7 \][/tex]

This simplifies to:

[tex]\[ 12.6 + b = 15.7 \][/tex]

Next, solve for \( b \) by isolating it on one side of the equation. Subtract \( 12.6 \) from both sides of the equation:

[tex]\[ b = 15.7 - 12.6 \][/tex]

Performing the subtraction, we get:

[tex]\[ b = 3.1 \][/tex]

Therefore, the length of the base \( b \) of the isosceles triangle is 3.1 centimeters.

Thus, the equation that can be used to find the length of the base when one of the longer sides is known is:

[tex]\[ 2a + b = 15.7 \][/tex]

And upon substituting \( a = 6.3 \):

[tex]\[ b = 15.7 - 12.6 \][/tex]

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