Answer:
The triangles are similar, because the ratio of its corresponding sides is equal
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal
so
Find the value of x
[tex]\frac{30}{6.3x+6}=\frac{20}{25} \\ \\30*25=20*(6.3x+6)\\ \\ 37.5=6.3x+6\\ \\6.3x=37.5-6\\ \\x=31.5/6.3\\ \\x=5\ units[/tex]
The value of the hypotenuse in the second triangle is
[tex](6.3x+6)=6.3*5+6=37.5\ units[/tex]
Applying the Pythagoras Theorem find the value of the second leg in both triangles
First triangle
[tex]h1^{2}=30^{2}-20^{2}\\ \\h1^{2} =500\\ \\h1=10\sqrt{5}\ units[/tex]
Second triangle
[tex]h2^{2}=37.5^{2}-25^{2}\\ \\h2^{2} =\frac{3,125}{4}\\ \\h2=\frac{25\sqrt{5}}{2}}\ units[/tex]
Verify the ratios of the corresponding sides
[tex]\frac{20}{25}=\frac{30}{37.5}=\frac{10\sqrt{5}}{\frac{25\sqrt{5}}{2}}[/tex]
[tex]0.8=0.8=0.8[/tex] -----> is true
therefore
The triangles are similar
