Finding value c using Pythagorean theorem:
[tex]c = \sqrt{{a}^{2} + {b}^{2} } [/tex]
[tex]c = \sqrt{ {8}^{2} + {15}^{2} } [/tex]
[tex]c = \sqrt{64 + 225} [/tex]
[tex]c = \sqrt{289} \\ \boxed{ \green{ \: \: c = 17 \: \: }}[/tex]
Finding the value of d:
[tex]d = \sqrt{ {f}^{2} - { e}^{2} } [/tex]
[tex]d = \sqrt{25 - 9} [/tex]
[tex]d = \sqrt{16} \\ \boxed{ \green{ \: \: d = 4 \: \: }} \\ \\ [/tex]
c+d = 21
