Question

1. which is necessary to calculate the perimeter of a triangle?

a. the height of the triangle
b. the area of the triangle
c. the base of the triangle
d. the length of all three sides

Explanation:

Step1: Recall the definition of perimeter

Perimeter is the sum of the lengths of all sides of a figure.

Step2: Analyze for a triangle

For a triangle with side lengths \(a\), \(b\), and \(c\), the perimeter \(P=a + b+ c\). So, we need the lengths of all three sides.

• Option a: Height is used for area (\(A=\frac{1}{2}\times base\times height\)), not perimeter.
• Option b: Area formula (\(A=\frac{1}{2}\times base\times height\)) doesn't directly give perimeter.
• Option c: Knowing just the base is insufficient as we need all three side - lengths.
• Option d: Since \(P=a + b + c\) (where \(a\), \(b\), \(c\) are side lengths), the length of all three sides is necessary.

Answer:

D. The length of all three sides