Question

shirley is drawing triangles that have the same area. the base of each triangle varies inversely with the height. what are the possible base and height of a second triangle if the first triangles base is 14 and its height is 6? 50 and 34 120 and 70 12 and 7 12 and 8

Explanation:

Step1: Calculate area of first triangle

The area of a triangle is $A=\frac{1}{2}bh$. For the first triangle with $b = 14$ and $h = 6$, $A=\frac{1}{2}\times14\times6=42$.

Step2: Check each option for second - triangle

Since the areas are equal and $A=\frac{1}{2}bh = 42$, then $bh=84$.

• For option 1: If $b = 50$ and $h = 34$, then $bh=50\times34 = 1700

eq84$.

• For option 2: If $b = 120$ and $h = 70$, then $bh=120\times70=8400

eq84$.

• For option 3: If $b = 12$ and $h = 7$, then $bh=12\times7 = 84$.
• For option 4: If $b = 12$ and $h = 8$, then $bh=12\times8=96

eq84$.

Answer:

12 and 7