Question

Find the missing side.

1) 2304
2) 3600
3) 1296
4) 36

Answer 1

• 36. (Option 4)

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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 (Base) {}^(2) + (Perpendicular {)}^(2) = (Hypotenuse {)}^(2) }}} \\ \\`

Here,

• The base (BC) is a

• The perpendicular (AC) is 48

• The hypotenuse (AB) is 60.

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So, substituting the values in the formula we get :

`\\ {\longrightarrow \pmb{\sf {\qquad (a) {}^(2) + (48 {)}^(2) = ( 60{)}^(2) }}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad (a) {}^(2) = ( 60{)}^(2) - (48 {)}^(2)}}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad (a) {}^(2) =3600 - 2304}}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad (a) {}^(2) =1296}}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad a = √(1296)}}} \\ \\`

`{\longrightarrow \pmb{\frak {\qquad a = 36 }}} \\ \\`

Therefore,

• The measure of the third side (a) is 36.

Answer 2

heya! ^^

here , we've been given a right angled triangle along with the measure of two of its sides.

and , we've to find the measure of its third side.

so , we'll be using Pythagoras Theorem to find the measure of the third side.

but first , let's take a look at what Pythagoras Theorem is-

Pythagoras theorem states that the square of the hypotenuse of the triangle is equal to the sum of squares of the remaining two sides.

according to the figure ,

side AB = hypotenuse = 60 cm

side AC = perpendicular = 48 cm

side BC = base = a

now by using Pythagoras Theorem ,

`H {}^(2) = P {}^(2) + B {}^(2) \\ \\ (60) {}^(2) = (48) {}^(2) + a {}^(2) \\ \\ 3600 = 2304 + a {}^(2) \\ \\ a {}^(2) = 1296 \\ \\ a = √(1296) \\ \\ a = 36`

therefore ,

option ( 4 ) 36 is correct.

hope helpful :D