Question

A person wishes to fit three rods together in the shape of a right angled triangle so that the hypotenuse is to be $4$ cm longer than the base and $8$ cm longer than the altitude. The lengths of the rods are:

• A. $3$ cm, $4$ cm, $5$ cm
• B. $1.5$ cm, $2$ cm, $2.5$ cm
• C. $6$ cm, $8$ cm, $10$ cm
• D. $12$ cm, $16$ cm, $20$ cm

Answer 1

The correct option is D $12$ cm, $16$ cm, $20$ cm

Let the base be $x$ cm

Thus, perpendicular is $(x-4)$ cm and hypotenuse is $(x+8)$ cm

By Pythagoras theorem, we have

$(\text{Hypotenuse}{)}^2=(\text{perpendicular}{)}^2+(\text{base}{)}^2$

$(x+4{)}^2=(x-4{)}^2+x^2$

$\Rightarrow x^2+16+8x=x^2+16-8x+x^2$

$\Rightarrow 16x=x^2$

$\Rightarrow x=16$

Then, for $x=16$

Hypotenuse $=20$ cm

Base $=16$ cm

Perpendicular $=12$ cm

Hence, option D is correct.