Question

Can someone pls help me? I don't understand how to do this. Would really appreciate it! ​

Answer 1

Answers:

• a = 21
• b = 42*sqrt(2)
• h = 14*sqrt(2)

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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)