This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2ab = 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?
The Correct Answer and Explanation is:
Correct Equation:
If one of the longer sides is 6.3 centimeters, then the correct equation to find the length of the base bbb is:2(6.3)+b=15.72(6.3) + b = 15.72(6.3)+b=15.7
Explanation
An isosceles triangle has two sides of equal length. In this case, the two equal sides are labeled as aaa, and the base is labeled as bbb. The perimeter of any triangle is the sum of the lengths of its three sides. Therefore, the perimeter of this triangle is calculated as:Perimeter=a+a+b=2a+b\text{Perimeter} = a + a + b = 2a + bPerimeter=a+a+b=2a+b
We are told that the perimeter of the triangle is 15.7 centimeters. So we can write:2a+b=15.72a + b = 15.72a+b=15.7
This is the correct model for the perimeter of an isosceles triangle when two sides are the same length. However, the original equation given in the problem is:2ab=15.72ab = 15.72ab=15.7
This equation is incorrect for modeling the perimeter of a triangle. It appears to represent something else, perhaps a product rather than a sum. Since perimeter is found by adding side lengths, multiplication is not appropriate here. We should correct the model to reflect the correct relationship:2a+b=15.72a + b = 15.72a+b=15.7
Now, we are told that one of the longer sides is 6.3 centimeters. Since the two equal sides are both 6.3 centimeters, we can substitute a=6.3a = 6.3a=6.3 into the corrected equation:2(6.3)+b=15.72(6.3) + b = 15.72(6.3)+b=15.7
Now solve for bbb:12.6+b=15.712.6 + b = 15.712.6+b=15.7b=15.7−12.6=3.1b = 15.7 – 12.6 = 3.1b=15.7−12.6=3.1
So, the base of the triangle is 3.1 centimeters. The correct equation to find the base when the equal sides are 6.3 centimeters each is:2(6.3)+b=15.72(6.3) + b = 15.72(6.3)+b=15.7
