The lengths of the sides of a triangle are in the ratio 3 : 4...

Brisa Lyons

Brisa Lyons

Answered

2022-12-28

The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.

Answer & Explanation

Josselyncx6

Josselyncx6

Expert

2022-12-29Added 4 answers

Ratio in the sides of a triangle= 3 : 4 : 5
Perimeter = 144 cm
Sum of ratios= 3+4+5=12
First side = 144 12 × 3 = 36   c m
Second side = 144 12 × 4 = 48   c m
Third side = 144 12 × 5 = 60   c m
s = Perimeter 2 = 144 2 = 72 Area = s ( s a ) ( s b ) ( s c ) = 72 ( 72 36 ) ( 72 48 ) ( 72 60 ) = 72 × 36 × 24 × 12 = 12 × 12 × 3 × 2 = 864   c m 3
The length of the altitude on the longest side measures 60 cm, or
Area × 2 Base = 864 × 2 60 = 1728 60 = 288 10 = 28.8   c m

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