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What is the length of the hypotenuse of the triangle?


Triangle A B C. Side A C is 7 feet and side C B is 4 feet. Hypotenuse A B is unknown.
StartRoot 22 EndRoot ft
StartRoot 33 EndRoot ft
StartRoot 57 EndRoot ft
StartRoot 65 EndRoot ft

What Is The Length Of The Hypotenuse Of The Triangle Triangle A B C Side A C Is 7 Feet And Side C B Is 4 Feet Hypotenuse A B Is Unknown StartRoot 22 EndRoot Ft class=

Sagot :

Answer:

The last answer [tex]\sqrt{65}[/tex]

Step-by-step explanation:

[tex]7^2+4^2 = 65[/tex]

The formula to find it is [tex]a^2+b^2=c^2[/tex]

so [tex]\sqrt{65}[/tex] is correct

Answer:

  • √65 ft (Option D)

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Step-by-step explanation:

  • This is Right Angled Triangle.

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We'll solve this using the Pythagorean Theorem.

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  • AC = 7ft which is the Base.

  • BC = 4 ft which is the Perpendicular.

  • AB is the Hypotenuse.

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We know that,

[tex]{ \longrightarrow \pmb{\qquad \: (AB) {}^{2} = (AC) {}^{2} + ( BC) {}^{2}}}[/tex]

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[tex]{ \longrightarrow \sf{\qquad \: (AB) {}^{2} = (7) {}^{2} + ( 4) {}^{2}}}[/tex]

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[tex]{ \longrightarrow \sf{\qquad \: (AB) {}^{2} = 49 + 16}}[/tex]

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[tex]{ \longrightarrow \sf{\qquad \: (AB) {}^{2} = 65}}[/tex]

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[tex]{ \longrightarrow \sf {\pmb {\qquad \: AB}}} = \pmb{ \frak{\sqrt{65}}}[/tex]

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Therefore,

  • The length of the Hypotenuse (AB) is √65 ft
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