Question

Susan is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be 4 inches. The area of the pennant must be at least 12 square inches. (The pennant has to be seen in the photo.) Write an Inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular pennant.

Answer 1

Susan is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be 4 inches. The area of the pennant must be at least 12 square inches. (The pennant has to be seen in the photo.) Write an Inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular pennant.​

Remember that

the area of the triangle is

`A=(1)/(2)b\cdot h`

we have

b=4 in

at least -----> is greater than or equal to

so

`A\ge12\text{ in2}`

therefore

`\begin{gathered} (1)/(2)\cdot(4)\cdot h\ge12 \\ \text{solve for h} \\ 2h\ge12 \\ h\ge6\text{ in} \end{gathered}`

the height of triangle must be greater than or equal to 6 inches