Question

Please help pethagriem entherum

Answer 1

Hey ! there

Answer:

• 13 is the answer .

Explanation:

In this question we are provided with right angle triangle having hypotenuse ( longest side ) = c , perpendicular = 5 and base = 12 . And we are asked to find the length of missing side i.e. hypotenuse and if necessary we have to round it off to 2 decimal places.

We can find the missing side by using Pythagorean Theorem . It states that sum of squares of perpendicular and base is equal to square in a right angle triangle that is ,

`\: \qquad \: \qquad \: \underline{\boxed{ \frak{H {}^(2) = P {}^(2) + B {}^(2) }}}`

Where ,

• H refers to Hypotenuse

• P refers to Perpendicular

• B r refers to Base

SOLUTION : -

Substituting value of hypotenuse as c , perpendicular as 5 and base as 12 in formula :

`\quad \longmapsto \qquad \: (c) {}^(2) = (5) {}^(2) + (12) {}^(2)`

Squaring 5 and 12 :

`\quad \longmapsto \qquad \:(c) {}^(2) = 25 + 144`

Adding 25 and 144 :

`\quad \longmapsto \qquad \:(c) {}^(2) = 169`

Applying square root to both sides :

`\quad \longmapsto \qquad \: \sqrt{(c) {}^(2) } = √(169)`

On simplifying , We get :

`\quad \longmapsto \qquad \orange{\underline{\boxed{\frak{c = 13}}}} \quad \bigstar`

• Henceforth , ❝ 13 ❞ is the length of missing side .

Verifying : -

Now we are checking our answer by putting all values in formula . So ,

• ( 13 )² = ( 5 )² + ( 12 )²

• 169 = 25 + 144

• 169 = 169

• L.H.S = R.H.S

• Hence, Verified .

Therefore , our answer is correct .

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Answer 2

• 13

`\:`

Step-by-step explanation :

Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.

We'll find the measure of third side with the help of the Pythagorean theorem,

`\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^(2)= (Base) {}^(2) + (Perpendicular {)}^(2) }}} \\ \\`

Here,

• The Base is 12

• The Perpendicular is 5

• The Hypotenuse is c.

`\:`

So, substituting the values in the formula we get :

`\\ {\longrightarrow \pmb{\sf {\qquad (c {)}^(2)= (12) {}^(2) + (5 {)}^(2) }}} \\`

`{\longrightarrow \pmb{\sf {\qquad (c {)}^(2)= 144 + 25 }}} \\`

`{\longrightarrow \pmb{\sf {\qquad (c {)}^(2)= 169 }}} \\`

`{\longrightarrow \pmb{\sf {\qquad c = √(169) }}} \\`

`{\longrightarrow \pmb{\sf {\qquad c= 13 }}}\\ \\`

Therefore,

• The measure of the third side (c) is 13