Question 978473: A triangle has sides measuring 13 cm, 13 cm, and 10 cm. A second triangle is drawn with sides measuring 13 cm, 13 cm, and x cm, where x is a whole number other than 10. If the two triangles have equal areas, what is the value of x? Show your work.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A triangle has sides measuring 13 cm, 13 cm, and 10 cm. A second triangle is drawn with sides measuring 13 cm, 13 cm, and x cm, where x is a whole number other than 10. If the two triangles have equal areas, what is the value of x?
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Area = b*h/2
Sides a = 13, b = 13, c = 10
Area = b*h/2
b = 1 of the 13 cm sides.
Angle C is between the 2 13 cm sides
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Use the Cosine Law.
10^2 = 13^2 + 13^2 - 2*13*13*cos(C)
cos(C) = 238/338
Angle C =~ 45.2397 degs
To have the same value of h, angle C' for side x is the supplement of C = 134.76 degs
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Use the Cosine Law to find x:
x^2 = 13^2 + 13^2 - 2*13*13*cos(134.76)
x^2 = 338 + 338*cos(C) = 338 + 238 = 576
x = 24 cm
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