[tex]m=5\text{ }\sqrt[]{5}[/tex]
STEP - BY - STEP EXPLANATION
What to find?
The value of m.
To find the value of m, we take the proportion of the sides of the triangles.
That is;
adjacent of the bigger triangle/hypotenuse of the bigger triangle = adjacent of the smaller triangle / hypotenuse of the smaller triangle.
That is;
[tex]\frac{m}{20+5}=\frac{5}{m}[/tex][tex]\frac{m}{25}=\frac{5}{m}[/tex]
Cross-multiply
[tex]m^2=25\times5[/tex]
Take the square root of both-side of the equation.
[tex]m=\sqrt[]{25\times5}[/tex][tex]m=5\sqrt[]{5}[/tex]
