Answer:
x = 18
m = 21.2
p = 31.8
Step-by-step explanation:
The ratio of the left-side length to the bottom-side length is the same for both triangles:
x/11.2 = (x +27)/28
28x = 11.2(x +27) = 11.2x +302.4 . . . . . multiply by 11.2·28
16.8x = 302.4 . . . . . . . subtract 11.2x
x = 18 . . . . . . . . . . . . divide by 16.8
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The length of m can be found using the Pythagorean theorem. The sum of the squares of the legs is the square of the hypotenuse.
x^2 +11.2^2 = m^2
m = √(324 +125.44) = √449.44 = 21.2
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The length of p can also be found using the Pythagorean theorem. We prefer the proportion ...
p/27 = m/x
p = 27(21.2/18) = 31.8
The lengths of the unknown sides in the figure are ...
x = 18
m = 21.2
p = 31.8
