Question

see this attachment and answer ​

Answer 1

Answer:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. ... The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

Answer 2

$\huge\red{\underline{{\bf ᴀ}}}\huge\orange{\underline{{\bf ɴ}}}\huge\green{\underline{{\bf s}}}\huge\blue{\underline{{\bf ᴡ}}}\huge\purple{\underline{{\bf ᴇ}}}\huge\pink{\underline{{\bf ʀ}}} </p><p>$

➙Pʏᴛʜᴏɢᴏʀᴀs Tʜᴇᴏʀᴇᴍ sᴛᴀᴛᴇs ᴛʜᴀᴛ ɪɴ ᴀ ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴛʀɪᴀɴɢʟᴇ, ᴛʜᴇ sqᴜᴀʀᴇ ᴏғ Hʏᴘᴏᴛᴇɴᴜsᴇ ɪs ᴇqᴜᴀʟ ᴛᴏ ᴛʜᴇ sᴜᴍ ᴏғ sqᴜᴀʀᴇs ᴏғ ɪᴛs Bᴀsᴇ ᴀɴᴅ Hᴇɪɢʜᴛ.

➙Cᴏɴᴠᴇʀsᴇ ᴏғ Pʏᴛʜᴀɢᴏʀᴀs Tʜᴇᴏʀᴇᴍ:-

Tʜɪs ɪs ᴊᴜsᴛ ᴛʜᴇ ᴄᴏɴᴠᴇʀsᴇ ᴀɴᴅ ᴅᴇʀɪᴠᴀᴛɪᴠᴇ ᴏғ Pʏᴛʜᴀɢᴏʀᴀs Tʜᴇᴏʀᴇᴍ. Iᴛ sᴛᴀᴛᴇs ᴛʜᴀᴛ ɪғ ᴛʜᴇ sqᴜᴀʀᴇ ᴏғ Hʏᴘᴏᴛᴇɴᴜsᴇ ɪs ᴇwᴜᴀʟ ᴛᴏ ᴛʜᴇ sᴜᴍ ᴏғ sqᴜᴀʀᴇs ᴏғ ɪᴛs Bᴀsᴇ ᴀɴᴅ Hᴇɪɢʜᴛ, ᴛʜᴇɴᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ɪs Rɪɢʜᴛ Aɴɢʟᴇᴅ Tʀɪᴀɴɢʟᴇ.

Tʜɪs ᴛʜᴇᴏʀᴇᴍ ᴄᴀɴ ʙᴇ ғᴏʀᴍᴜʟᴀᴛᴇᴅ ᴀs⤵

$\;\large{\boxed{\bf{\purple{(Hypotenuse)^{2}\;=\;(Base)^{2}\;+\;(Height)^{2}}}}}$

Fʀᴏᴍ ᴛʜɪs ᴍᴀɪɴ ғᴏʀᴍᴜʟᴀ, ᴡᴇ ᴄᴀɴ ᴅᴇʀɪᴠᴇ⤵

$\;\bf{\green{\rightarrow\;\;(Hypotenuse)^{2}\;-\;(Base)^{2}\;=\;(Height)^{2}}}$

$\;\bf{\green{\rightarrow\;\;(Hypotenuse)^{2}\;-\;(Height)^{2}\;=\;(Base)^{2}}}$