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Ashley 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 8 inches. The area of the pennant must be at least 28 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.

Sagot :

Consider Ashley's pennant to have the following shape

In our case, b=8 inches. The area of a triangle of base b and height h is given by the expression

[tex]\frac{b\cdot h}{2}[/tex]

Since b=8, we get

[tex]\frac{8\cdot h}{2}=4\cdot h[/tex]

Now, this expression represents the area of the triangle. We are told that this area should be at least 28 squared inches, then we have the inequality

[tex]4\cdot h\ge28[/tex]

If we divide by 4 on both sides, we get

[tex]h\ge\frac{28}{4}=7[/tex]

So the height of the pennant should be at least 7 inches

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