As the exercise says, the triangles are similar. So, we can set up proportions between correspondent sides.
In order to solve for x we can set up the proportion between the horizontal and vertical sides:
[tex]28\div 11.2 = 27+x \div x[/tex]
Solving this proportion for x implies [tex]x=18[/tex]
Now you can solve for m and p using the pythagorean theorem, because both triangles are right:
[tex]m = \sqrt{18^2+11.2^2} =21.2[/tex]
Then, we know that the hypothenuse of the big triangle is m+p, so we have
[tex]m+p=\sqrt{(18+27)^2+28^2} = 53[/tex]
which implies
[tex]p = 53-p = 53-21.2=31.8[/tex]
The ratio of the given to similar triangles is 0.4. value of the x, m, and p is 18, 21.2, and 31.8.
Similar triangles are triangles whose corresponding sides are in ratio, while the corresponding angles are of equal measure.
As the two sides of the triangles are already given, therefore, the ratio of these two triangles are,
[tex]\dfrac{11.2}{28} = \dfrac{2}{5}[/tex]
As we already know the ratio of the two triangles, therefore,
[tex]\dfrac{x}{27+x} = \dfrac{2}{5}\\\\5x = 54 + 2x\\\\5x-2x = 54\\\\3x = 54\\\\x = 18[/tex]
Hence, the value of x is 18.
As the given triangle is a right-angled triangle, therefore, we can use the Pythagorean theorem to find the value of m,
[tex](Hypotenuse)^2 = (Perpendicular)^2+(Base)^2\\\\m^2 = x^2 + (11.2)^2\\\\m^2 = 18^2 + 11.2^2\\\\m^2 = 324+125.44\\\\m^2 = 449.44\\\\m = 21.2[/tex]
Thus, the value of side m is 21.2 units.
The value of m and p can be found using the same ratio, we already have for similar triangles,
[tex]\dfrac{m}{m+p} = \dfrac{2}{5}\\\\\dfrac{21.2}{21.2+p} = \dfrac{2}{5}\\\\106= 42.4 + 2p\\\\p = 31.8[/tex]
Thus, the value of the x, m, and p is 18, 21.2, and 31.8.
Learn more about Similar Triangles:
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