Answer:
1. [tex]x^{2} =24^{2}+18^{2}[/tex]
[tex]x^{2} =900[/tex]
[tex]x=30[/tex]
2. [tex]10^{2} =x^{2}+6^{2}[/tex]
[tex]x^{2}=10^{2}-6^{2}[/tex]
[tex]x^{2}=64[/tex]
[tex]x=8[/tex]
3. [tex]5^{2} =x^{2}+3^{2}[/tex]
[tex]x^{2}=5^{2}-3^{2}[/tex]
[tex]x^{2}=16[/tex]
[tex]x=4[/tex]
4. First, find the common side (red line)
[tex]15^{2} =c^{2}+9^{2}[/tex]
[tex]c^{2}=15^{2}-9^{2}[/tex]
[tex]c^{2}=144[/tex]
[tex]c=12[/tex]
Since these two triangles are similar, x can be solved as
[tex]\frac{x}{12} =\frac{12}{9}[/tex]
[tex]x=16[/tex]
5. Since these two triangles are similar, x can be determined as
[tex]\frac{x}{12} =\frac{12}{16}[/tex]
[tex]x=9[/tex]
