Answer: x = 7*sqrt(30)
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Step-by-step explanation:
Let h be the height of largest triangle. It is the vertical segment in the diagram.
The three triangles are similar, so we can form the proportion shown below to solve for h.
7/h = h/35
7*35 = h*h
245 = h^2
h = sqrt(245)
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Now focus on the medium-sized triangle on the right. It has legs of 35 and sqrt(245). The hypotenuse is x.
Use the pythagorean theorem.
a^2 + b^2 = c^2
(sqrt(245))^2 + (35)^2 = x^2
245 + 1225 = x^2
x^2 = 1470
x = sqrt(1470)
x = sqrt(49*30)
x = sqrt(49)*sqrt(30)
x = 7*sqrt(30)