Question

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

Answer 1

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,

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

Substituting the given values in the formula :

`\qquad\sf{ \dashrightarrow{ ( BC ) {}^(2) = (AB) {}^(2) + (AC ) {}^(2) }}`

`\qquad\sf{ \dashrightarrow{ ( BC ) {}^(2) = (6) {}^(2) + (8 ) {}^(2) }}`

`\qquad\sf{ \dashrightarrow{ ( BC ) {}^(2) = 36 + 64 }}`

`\qquad\sf{ \dashrightarrow{ ( BC ) {}^(2) = 100 }}`

`\qquad\sf{ \dashrightarrow{ BC {} = √(100) }}`

`\qquad\sf{ \dashrightarrow{ BC {} = 10 }}`

⠀

• Therefore, BC = 10 cm