SOLUTION: A window in the shape of a rectangle surmounted by an isosceles triangle is to have a width of 75cm and a total height of 180cm. If the total area of the window is to be 12,000cm^2

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Since this is a triangle on top of a rectangle, where the total height of the window is 180, let x = height of the triangle, and 180 - x = height (or length) of the rectangle, where 75 is the base of the triangle and the width of the rectangle.

Total area = area triangle + area rectangle
Total area = bh/2 + WL
12000 = (75*x)/2 + (75)(180-x)

Multiply both sides by 2 to clear the fraction:
24000 = 75x + 150(180-x)
24000 = 75x + 27000 - 150x
24000 = -75x + 27000

Subtract 27000 from each side:
-3000 = -75x

Divide both sides by -75
cm

Check: Area Triangle =
Area Rectangle =

Total Area =

R^2 at SCC