Question

In $\Delta ABC,\angle B={90}^{\circ }$. Find the sides of the triangle, if AB = (x + 2) cm, BC = (x + 4) cm and AC = (x + 6) cm.

• A. 3, 4 and 5
• B. 6, 8 and 10
• C. 5, 12, and 13
• D. None

Answer 1

The correct option is B

6, 8 and 10

In right - angled triangle $\Delta ABC$,

$\Rightarrow (x+6{)}^2=(x+4{)}^2+(x+2{)}^2$

$\Rightarrow x^2+12x+36=x^2+8x+16+x^2+4x+4$

$\Rightarrow 12x+36=12x+x^2+20$

$\Rightarrow 16=x^2$

$\Rightarrow x^2=\sqrt{16}=4cm$

$\therefore$ Sides of the triangle are $x+2=4+2=6cm$

$x+4=4+4=8cm$

$x+6=4+6=10cm$