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A triangle with an area of 10 square meters has a base of 4 meters. A similar triangle has an area of 90 square meters. What is the height of the larger triangle?
10 = (1/2)4h → 20 = 4h → h = 5 So the base of the first triange is 4m and the height is 5m Note that the area of our new triangle is 9 times the area of the old then each dimension will be sqrt(9) = 3 times as much as the old so The base of the new triangle will be 4*3 = 12m And the height will be 5 * 3 = 15m Proof: A = (1/2)(12)(15) = (1/2) * 180 = 90 m^2
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