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

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

 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

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

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.

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$\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet$

$\pmb{\tt{Question4}}$

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

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

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

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

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

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

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

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

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

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

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

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

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

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