Question

the area formula for a triangle is ( a = \frac{1}{2}bh ). the area of the triangle can be described by the inequality ( 98 leq a leq 102 ). the base of the triangle is ( 2x ) and the height is ( 8.5 ). what is the maximum value that ( x ) can be in this situation?
answer attempt 1 out of 4
additional solution no solution

Explanation:

Step1: Substitute base and height into area formula

The base \( b = 2x \) and height \( h = 8.5 \). The area formula is \( A=\frac{1}{2}bh \), so substitute the values: \( A=\frac{1}{2}(2x)(8.5) \). Simplify this: \( \frac{1}{2}\times2x\times8.5 = 8.5x \).

Step2: Use the maximum area to find x

We want the maximum value of \( x \), so we use the maximum area \( A = 102 \) (since \( 98\leq A\leq102 \), the largest \( A \) gives the largest \( x \)). Set up the equation \( 8.5x = 102 \).

Step3: Solve for x

To solve for \( x \), divide both sides of the equation by \( 8.5 \): \( x=\frac{102}{8.5} \). Calculate this: \( \frac{102}{8.5}=12 \).

Answer:

12