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3 years ago

Find the missing side of the triangle. Round your answer to the nearest tenth if necessary.

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

7 0

Answer:

Step-by-step explanation:

pythagoras theorem

a^2+b^2=c^2

12^2+x^2=13^2

144+x^2=169

x^2=169-144

x= $\sqrt{25$

x=5

egoroff_w [7]3 years ago

3 0

$\huge\bold{Given:}$

Length of the base = 12 km.

Length of the hypotenuse = 13 km. $\huge\bold{To\:find:}$

✎ The missing side (perpendicular) '' $x$ " of the triangle.

$\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}$

The missing side " $x$ " of the triangle is $\boxed{5\:km}$ .

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}$

Using Pythagoras theorem, we have

$({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ ⇢ {x}^{2} + ({12 \: km})^{2} = ( {13 \: km})^{2} \\ ⇢ {x}^{2} + 144 \: {km}^{2} = 169 \: {km}^{2} \\ ⇢ {x}^{2} = 169 \: {km}^{2} - 144 \: {km}^{2} \\ ⇢ {x}^{2} = 25 \: {km}^{2} \\ ⇢ x = \sqrt{25 \: {km}^{2} } \\ ⇢x = 5 \: km$

$\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:side\:"x"\:is\:5\:km.}$

$\huge\bold{To\:verify :}$

$({5 \: km})^{2} + ({12 \: km})^{2} =( {13 \: km})^{2} \\ ⇝25 \: {km}^{2} + 144 \: {km}^{2} = 169 \: {km}^{2} \\ ⇝169 \: {km}^{2} = 169 \: {km}^{2} \\ ⇝L.H.S.=R. H. S$

Hence verified. ✔

$\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘$

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