Question

maria designs a triangle with an area of 32 square centimeters. what could be the base and height of marias triangle? move the correct answer to each box. not all answers will be used. 64 4 8 10 32 16 marias triangle could have a base of centimeters and a height of centimeters.

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\), where \(A\) is the area, \(b\) is the base, and \(h\) is the height. Given \(A = 32\) square centimeters, we can rewrite the formula as \(b\times h=2A\). So \(b\times h=2\times32 = 64\).

Step2: Find pairs of numbers from the given set that multiply to 64

We check the products of the given numbers:

• \(4\times16=64\)
• \(8\times8 = 64\) (but we assume distinct base and height if possible, and 8 is given once. Also, if we consider non - distinct, 8 and 8 is a valid pair. But looking at the options, 4 and 16 is a more likely pair as per the problem's nature of using distinct numbers from the given set)

Answer:

Maria's triangle could have a base of \(4\) centimeters and a height of \(16\) centimeters (or a base of \(16\) centimeters and a height of \(4\) centimeters or a base of \(8\) centimeters and a height of \(8\) centimeters)