Question

answer the following question​

Answer 1

$hypotenuse \: = \sqrt{(perependicular) {}^{2} + (base) {}^{2} } \\ \\ so \: x + 5 = \sqrt{(x + 3) {}^{2} + 36} \\ \\ x + 5 = \sqrt{x {}^{2} + 6x + 9 + 36} = \sqrt{x {}^{2} + 6x + 45} \\ \\ on \: squaring \: both \: sides \\ \\ (x + 5) {}^{2} = x {}^{2} + 6x + 45 \\ \\ = x {}^{2} + 25 + 10x = x {}^{2} + 6x + 45 \\ \\ cancelling \: similiar \: terms \\ \\ 10x + 25 = 6x + 45 \\ \\ transposing \: like \: terms \: on \: same \: side \: \\ \\ 10x - 6x = 45 - 25 \\ \\ = 4x = 20 \\ \\ \maltese \huge\: \fbox \red {x = 5}$

Then length of third side = x+3 = 5+3 = 8 cm

Answer 2

Step-by-step explanation:

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