SOLUTION: The area of a trapezoid is 3440 square inches, and the lengths of its parallel sides are in a 3:5 ratio. A diagonal divides the trapezoid into two triangles. What are their areas?

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Question 1158583: The area of a trapezoid is 3440 square inches, and the lengths of its parallel sides are in a 3:5 ratio. A diagonal divides the trapezoid into two triangles. What are their areas?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
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area+of%28+triangle%29+CAD+%2FArea+of+%28triangle%29+ACD+=+3%5E2%2F5%5E2 =9/25


= 34/25

=+Area+of+trapezoid%2FArea+of+%28triangle%29+ACD+=+34%2F25
Area of (triangle) ACD =25*3440/34 =2529 cm^2








Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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Triangles ADC and ABC have COMMON altitude; therefore, the ratio of their areas is the same as the ratio of their bases |AD| : |BC| = 3%2F5.


Since the sum od the areas of these triangles is 3440 square inches, 


    the area of the triangle ADC is  %283%2F%283%2B5%29%29%2A3440 = %283%2F8%29%2A3440 = 1290 sq. inches;


    the area of the triangle ABC is  %285%2F%283%2B5%29%29%2A3440 = %285%2F8%29%2A3440 = 2150 sq. inches.

Solved.

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