explain why the triangles are similar.​

Accepted Solution

Answer:The triangles are similar, because the ratio of its corresponding sides is equalStep-by-step explanation:we know thatIf two figures are similar, then the ratio of its corresponding sides is equalsoFind 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 trianglesFirst 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 truethereforeThe triangles are similar