Question

The sum of the sides of a right-angled triangle is 36 cm, whose hypotenuse is 15 cm. The difference between the other two sides of this triangle would be:

• A. 4 cm
• B. 3 cm
• C. 5 cm
• D. 2 cm

Answer 1

The correct option is B

3 cm

Consider $△ABC,right-angledatBLetAB=acm,BC=bcmandAC=ccmThen,byPythagorastheorem,a^2+b^2=c^{2}i.e.a^2+b^2={15}^2$
Given, AC = c = 15 cm
$i.e.a^2+b^2=225\to \left(i\right)Given,a+b+c=36i.e.a+b+15=36\Rightarrow a+b=21$
Squaring the above equation on both the sides, we get,
$(a+b{)}^2={21}^{2}i.e.a^2+b^2+2ab=441$
$i.e.2ab=216(\because a^2+b^2=225)\Rightarrow ab=108Now,weknowthat,(a-b{)}^2=a^2+b^2-2ab=225-216=9\therefore a-b=\pm 3$
$\therefore$ The difference between the other two sides of triangle ABC is 3 cm.