Question

16. The lengths of the sides of a triangle are
proportional to the numbers 5, 12, and 13
The largest side of the triangle exceeds the smallest side by 1.6 m. Find the area of the
triangle in m2

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Answer 1

Step-by-step explanation:

Ratio of sides of triangle= 5:12:13

let the sides be 5x,12x,13x

difference between the largest and the smallest side = 1.6 m

So, 13x - 5x= 1.6

8x= 1.6

x= 1.6/8

x= 1/5

therefore, sides of the triangle are 1m, 2.4m, 2.6m

To find the base and height of the triangle -

Pythagoras Theorem = a2 +b2= c2

So, 1^2+ 2.4^2 = 2.6^2

1+5.76= 6.76

So, 6.76= 6.76

Therefore the base and height of the triangle is 1m and 2.4m respectively

Area of triangle = 1/2×base×height

1/2×1×2.4= 1.2m

Therefore the area of the triangle is 1.2m