Question

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Answer 1

10.58

Explanation:

We are here given a right angled triangle in which two of the sides are 16 and 12 and we are interested in finding the third side x . We will use Pythagoras theorem here according to which the sum of squares of base and perpendicular is equal to the square of hypotenuse. so that,

`\longrightarrow\sf h^2 = p^2+b^2\\`

`\longrightarrow\sf x^2 + 12^2 = 16^2\\`

`\longrightarrow\sf x^2 = 256 - 144\\`

`\longrightarrow\sf x =√( 112)=\boxed{10.58}`

and we are done!

-Rishabh

Answer 2

`x=4√(7)=10.6\; \sf (nearest\;tenth)`

Explanation:

`\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}`

From inspection of the given right triangle:

• a = x
• b = 12
• c = 16

Substitute the given values into Pythagoras Theorem formula and solve for x:

`\implies x^2+12^2=16^2`

`\implies x^2+144=256`

`\implies x^2=112`

`\implies x=√(112)`

`\implies x=√(16 \cdot 7)`

`\implies x=√(16) √(7)`

`\implies x=4√(7)`

`\implies x=10.6\; \sf (nearest\;tenth)`