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To make his house more energy-efficient, Ernest is putting solar film on the large trapezoid-shaped window in his living room. The window has an area of 2525 square feet. The top of the window is 33 feet long, and the bottom is 77 feet long.\newlineWhich equation can you use to find how tall the window is, hh?\newlineChoices:\newline(A) 25=12h(3+7)25 = \frac{1}{2}h(3 + 7)\newline(B) 25=h(3+7)25 = h(3 + 7)\newlineHow tall is the window?\newlineWrite your answer as a whole number or decimal. Do not round.\newline____ feet\newline

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Q. To make his house more energy-efficient, Ernest is putting solar film on the large trapezoid-shaped window in his living room. The window has an area of 2525 square feet. The top of the window is 33 feet long, and the bottom is 77 feet long.\newlineWhich equation can you use to find how tall the window is, hh?\newlineChoices:\newline(A) 25=12h(3+7)25 = \frac{1}{2}h(3 + 7)\newline(B) 25=h(3+7)25 = h(3 + 7)\newlineHow tall is the window?\newlineWrite your answer as a whole number or decimal. Do not round.\newline____ feet\newline
  1. Identify Area Formula: To find the height of the trapezoid window, we need to use the area formula for a trapezoid, which is A=12×(b1+b2)×hA = \frac{1}{2} \times (b_1 + b_2) \times h, where b1b_1 and b2b_2 are the lengths of the two bases, and hh is the height. Here, b1=3b_1 = 3 feet, b2=7b_2 = 7 feet, and A=25A = 25 square feet.
  2. Calculate with Given Values: Plugging in the values into the trapezoid area formula, we get 25=12×(3+7)×h25 = \frac{1}{2} \times (3 + 7) \times h. Simplifying inside the parentheses, 3+7=103 + 7 = 10.
  3. Simplify Equation: Now, substituting back, we have 25=12×10×h25 = \frac{1}{2} \times 10 \times h, which simplifies to 25=5×h25 = 5 \times h.
  4. Divide to Find Height: To find hh, divide both sides by 55: h=255h = \frac{25}{5}.
  5. Final Calculation: Calculating the division, h=5h = 5.

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