Question

determine the length of the side of a square that has the same area of a triangle with a base length of 9 inches and a height of 8 inches.

reference sheet
diagrams and formulas: circle (a=πr², c=2πr), rectangle (a=lw), triangle (a=½bh), right triangle (c²=a²+b²), special right triangles (30-60-90, 45-45-90), rectangular prism (v=lwh), cylinder (v=πr²h), sphere (v=⁴⁄₃πr³), cone (v=⅓πr²h), pyramid (v=⅓lwh); text: the number of degrees of arc in a circle is 360. the number of radians of arc in a circle is 2π. the sum of the measures in degrees of the angles of a triangle is 180.

options:

• 6 inches
• 10 inches
• 36 inches
• 72 inches

Explanation:

Step1: Calculate triangle area

Using formula \( A = \frac{1}{2}bh \), substitute \( b = 9 \), \( h = 8 \):
\( A = \frac{1}{2} \times 9 \times 8 = 36 \) square inches.

Step2: Find square side length

Let square side be \( s \). Area of square: \( A = s^2 \).
Set \( s^2 = 36 \), solve for \( s \): \( s = \sqrt{36} = 6 \).

Answer:

6 inches