Question

Question 20
Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle?
a) 3 cm, 4 cm, 6 cm
b) 9 cm, 16 cm, 26 cm
c) 1.5 cm, 3.6 cm, 3.9 cm
d) 7 cm, 24 cm, 26 cm

Answer 1

The sides of right-angled triangle must satisfy Pythagoras theorem.
$(Hypotenuse{)}^2=(Base{)}^2+(Perpendicular{)}^2$
Let us check all the options
a) $(6{)}^2=(3{)}^2+(4{)}^2$
$36=9+1636\ne 25$

b) $(26{)}^2=(16{)}^2+(9{)}^2$
$676=256+81676\ne 337$

c) $(3.9{)}^2=(1.5{)}^2+(3.6{)}^2$
$15.21=2.25+12.96$
$15.21=15.21$ (satisfied)

d) $(26{)}^2=(7{)}^2+(24{)}^2$
$676=49+576676\ne 625$
Clearly, option (c) is correct.