Answers:
- a = 21
- b = 42*sqrt(2)
- h = 14*sqrt(2)
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Step-by-step explanation:
There are 3 right triangles here. They are all similar triangles allowing us to form the proportion
7/h = h/56
which solves to...
7/h = h/56
7*56 = h*h
392 = h^2
h^2 = 392
h = sqrt(392)
h = sqrt(196*2)
h = sqrt(196)*sqrt(2)
h = 14*sqrt(2)
Note: h is the geometric mean of 7 and 56.
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Use the pythagorean theorem to solve for 'a'. Focus on the smaller triangle on the left
7^2 + h^2 = a^2
7^2 + (sqrt(392))^2 = a^2
49 + 392 = a^2
441 = a^2
a^2 = 441
a = sqrt(441)
a = 21
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Then we can find b. Again use the pythagorean theorem. Focus on the largest right triangle this time.
a^2 + b^2 = (7+56)^2
21^2 + b^2 = 63^2
441 + b^2 = 3969
b^2 = 3969 - 441
b^2 = 3528
b = sqrt(3528)
b = sqrt(1764*2)
b = sqrt(1764)*sqrt(2)
b = 42*sqrt(2)