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ABC is a triangle, right-angled at A. If AB = 6 and AC = 8, find BC.

Sagot :

Given :

  • ABC is a right angled triangle at A where AB is 6cm, AC is 8cm.

To Find :

  • BC.

Solution :

  • Let the Base be AB cm, Perpendicular be AC cm and Hypotenuse be BC.

We know that,

[tex] \qquad \sf{ \pmb{(Hypotenuse ) {}^{2} = (Base) {}^{2} + (Perpendicular) {}^{2} }}[/tex]

Substituting the given values in the formula :

[tex] \qquad\sf{ \dashrightarrow{ ( BC ) {}^{2} = (AB) {}^{2} + (AC ) {}^{2} }}[/tex]

[tex] \qquad\sf{ \dashrightarrow{ ( BC ) {}^{2} = (6) {}^{2} + (8 ) {}^{2} }}[/tex]

[tex] \qquad\sf{ \dashrightarrow{ ( BC ) {}^{2} = 36 + 64 }}[/tex]

[tex] \qquad\sf{ \dashrightarrow{ ( BC ) {}^{2} = 100 }}[/tex]

[tex] \qquad\sf{ \dashrightarrow{ BC {} = \sqrt{100} }}[/tex]

[tex] \qquad\sf{ \dashrightarrow{ BC {} = 10 }}[/tex]

⠀

  • Therefore, BC = 10 cm

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