Question

the hypotenuse of a right triangle is 70 cm long if one of the remaining two side it is of length 8 cm find the length of the third side

Answer 1

${70 }^{2} = {8}^{2} + {x}^{2} \\ 4900 = 64 + {x}^{2} \\ 4900 - 64 = {x}^{2} \\4836 = {x}^{2} \\ x = \sqrt{4836} \\ \\ x = 69.54$
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Answer 2

Question:

The hypotenuse of a right triangle is 17 cm long if one of the remaining two sides is of length 8cm. Find the length of the third side

Answer:

Hence, the length of third side is 15cm.

Step-by-step Explanation:

Given:

The hypotenuse of a right triangle is 17cm long.

If one of the remaining two sides is of length 8cm.

To Find:

Length of 3rd side

Solution:

Let the 3rd side be x

$\begin{gathered}\\{\large {\underline{ \underline{ \sf{ \pmb{\orange{Using Pythagoras Theorem}}}}}}} \\ \\ :\implies \underline{ \boxed{ \frak{{(h)}^{2}={(a)}^{2}+{(b)}^{2}}}} \color{navy} \bigstar \\  \\   :\implies \sf{{(17)}^{2}={(8)}^{2}+{(x)}^{2}} \\  \\ :\implies \sf{289=64+{(x)}^{2}} \\  \\ :\implies \sf{289-64={(x)}^{2}} \\  \\ :\implies \sf{225={(x)}^{2}} \\  \\ :\implies \sf{\sqrt{225}=x} \\  \\ : \implies   \underline{\boxed{ \frak{x = 15 \: cm}}} \pink \bigstar  \\  \\ \sf \: ∴ \underline {Hence, the length of third side is  \textbf{ \textsf{15 cm}}} . \end{gathered}$