Answered

This isosceles triangle has two sides of equal length that are longer than the length of the base, $b$. The perimeter of the triangle is 15.7 centimeters. The equation $2 a+b=15.7$ 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$6.3+b=15.7$
B$12.6+b=15.7$
C$2 a+6.3=15.7$
D$2 a+12.6=15.7$

Verified Answer :

  • Identify the perimeter equation for the isosceles triangle: \(2a + b = 15.7\).
  • Substitute the given side length \(a = 6.3\) into the equation: \(2(6.3) + b = 15.7\).
  • Calculate the product: \(2 \times 6.3 = 12.6\).
  • State the final equation: \(12.6 + b = 15.7\).
  • Final Answer: \(\boxed{12.6 + b = 15.7}\).

Explanation

  1. Analyzing the Given Information

The perimeter of an isosceles triangle is defined as the sum of its three sides. Let \(a\) represent the length of the two equal sides and \(b\) represent the length of the base. The perimeter is given by the expression \(2a + b = P\). We are given that the perimeter is \(15.7 \text{ cm}\), so the governing equation is \(2a + b = 15.7\). We are also told that the length of one of the longer sides \(a\) is \(6.3 \text{ cm}\).

  1. Substituting the Given Value

To find the base length \(b\), we substitute the known value \(a = 6.3\) into the perimeter equation \(2a + b = 15.7\). This gives us:
\[2(6.3) + b = 15.7\]

  1. Simplifying and Identifying the Correct Equation

We simplify the equation by performing the multiplication \(2 \times 6.3\):
\[2 \times 6.3 = 12.6\]
Substituting this back into the equation yields:
\[12.6 + b = 15.7\]
This is the equation that allows us to solve for the base \(b\). Comparing this result with the provided options, we can see that \(12.6 + b = 15.7\) is the correct equation.

Examples

In geometry and construction, modeling the dimensions of objects is essential. For instance, if you are building a triangular roof truss that must be isosceles to ensure symmetry, you would use this same method. By knowing the perimeter constraints and the length of the rafters (the sides), you can calculate the necessary length of the base beam to ensure the structure meets your design requirements.

Related Questions