Question

Please help need answers

Answer 1

`\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet`

`\frak{Good\;Morning!!}`

`\pmb{\tt{Question\;1}}`

`\star\boldsymbol{\rm{Given-:}}`

• Side length = 7 cm,
• Side length = 5 cm.

`\star\boldsymbol{\rm{We're\;looking\;for-:}}`

• Side length = x

This is how it's done.

`\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet`

There's a special formula that we can use if we need to find the longest side of a right triangle. Fortunately, all of these triangles are right ones! Good.

The formula is.
`\boldsymbol{\rm{a^2+b^2=c^2}}`. This formula is known as Pythagoras' Theorem. This formula only works for right triangles.

Since we have a and b, we can just put in the values (7 for a and 5 for b), And then simplify!

`\boldsymbol{\rm{7^2+5^2=c^2}}` | 7^2 simplifies to 49, and 5^2 simplifies to 25

`\boldsymbol{\rm{49+25=c^2}}`. | add

`\boldsymbol{\rm{74=c^2}}` | square root both sides

`\boldsymbol{\rm{8.6=c}}}`. | the answer is given to 1 decimal place, as the problem required

`\orange\hspace{350pt}\above5`

`\pmb{\tt{Question\;2}}`

Once more, we're given two sides, and asked to find the third one,

which is still the longest side.

`\boldsymbol{\rm{a^2+b^2=c^2}}` is still the formula used here

Put in 5 for a and 3 for b.

`\boldsymbol{\rm{5^2+3^2=c^2}}` | 5^2 simplifies to 25, and 3^2 simplifies to 9

`\boldsymbol{\rm{25+9=c^2}}` | add

`\boldsymbol{\rm{34=c^2}}` | square root both sides

`\boldsymbol{\rm 5.8=c}}` | once again it's given to one decimal place

`\hspace{350pt}\above5`

`\pmb{\tt{Question\;3}}`

This problem is solved the exact same way

`\boldsymbol{\rm{a^2+b^2=c^2}}`

`\boldsymbol{\rm{8.2^2+4.7^2=c^2}}`

`\boldsymbol{\rm{67.24+22.09=c^2}}`

`\boldsymbol{\rm{89.33=c^2}}`

`\boldsymbol{\rm{9.5=c}}`, rounded to one D.P.

`\orange\hspace{300pt}\above2`

`\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet`

`\pmb{\tt{Question4}}`

Here we have the longest side and one side length-:

`\boldsymbol{\rm{4^2+b^2=7^2}}` | 4^2 simplifies to 16 and 7^2 simplifies to 49

`\boldsymbol{\rm{16+b^2=49}}` | subtract 16 from both sides

`\boldsymbol{b^2=33}` | square root both sides

`\boldsymbol{\rm{b=5.7}}`

`\orange\hspace{300pt}\above3`

`\pmb{\tt{Question\;5}}`

`\boldsymbol{\rm{3.8^2+b^2=7.9^2}}`

`\boldsymbol{\rm{14.44+b^2=62.41}}`

`\boldsymbol{\rm{b^2=47.97}}`

`\boldsymbol{\rm{b=6.9}}`

`\orange\hspace{300pt}\above3`

`\pmb{\tt{Question\;6}}`

`\boldsymbol{\rm{a^2+6.1^2=7.3^2}}`

`\boldsymbol{\rm{a^2+37.21=53.29}}`

`\boldsymbol{\rm{a^2=16.08}}`

`\boldsymbol{\rm{a=4.0}}`

`\pmb{\tt{done~!!!}}`

`\orange\hspace{300pt}\above3`