Question

The sides of a different right-angled triangle are in the ratio 3:4:5
a) The length of the shortest side is 7.8 cm
calculate the length of the longest side.
b) Calculate the smallest angle in this triangle.

Answer 1

(a)-Let,

Three sides of a triangle be 3x, 4x, 5x.

Solution :-

Smallest side=3x

3x=7.8

x=7.8/3

=2.6cm

Length of another two sides:-

Second side=4x=4*2.6=10.4cm

Third side=5x=5*2.6=13cm

Hence, Longest side =Third side=13cm.

(b)- Let,

Three angles of a triangle be 3x degree, 4x degree, 5x degree.

We know that sum of all angles of a triangle =180 degree

3x+4x+5x=180 degree

12x=180 degree

x=180/12

=15 degree.

Measure of Angles-

First angle=3x degree =3*15=45 degree

Second angle=4x degree=4*15=60 degree

Third angle=5x degree =5*15=75 degree.

Hence, Smallest Angle=First angle=45 degree.