Question

Find the value of x in the triangle shown below

Answer 1

D

Explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of thesquares on the other two sides, that is

x² + 8² = 9²

x² + 64 = 81 ( subtract 64 from both sides )

x² = 17 ( take square root of both sides )

x =
`√(17)`

Answer 2

• √17 (Option D)

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Explanation:

• This is Right Angled Triangle.

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We'll solve this using the Pythagorean Theorem.

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Let,

• x be BC, where BC is the Perpendicular.

• 8 be AB, where AB is the Base.

• 9 be AC, where AC is the Hypotenuse.

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We know that,

`{ \longrightarrow \pmb{\qquad \: (AB) {}^(2) +( BC) {}^(2) = (AC) {}^(2) }}`

`{ \longrightarrow \sf \qquad \: (8) {}^(2) +( x) {}^(2) = (9) {}^(2) }`

`{ \longrightarrow \sf \qquad \: ( x) {}^(2) = (9) {}^(2) - (8) {}^(2)}`

`{ \longrightarrow \sf \qquad \: ( x) {}^(2) = 81 - 64}`

`{ \longrightarrow \sf \qquad \: ( x) {}^(2) = 17}`

`{ \longrightarrow \it \qquad \pmb {x = √(17 \: \: ) } }`

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Therefore,

• The value of x is √17 .