A right-angled triangle has a perimeter of 90 cm. The lengths of its three sides are in ratio 5:12:13. Calculate the area of this triangle.

Question

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Answer 1

Since the sides are in the ratio 5:12:13 and the perimeter is 90 cm, we can determine the length of the sides as follows:

 

5x + 12x + 13x = 90 cm

 

30x = 90 cm

 

x = 3 cm

 

So the sides of the triangle are 15 cm, 36 cm, and 39 cm.  The 39 cm side is the hypotenuse, so the area is:

 

Area = (1/2)*Base*Height = (1/2)*(15)*(36) = 270 cm²

Answer 2

The perimeter of a triangle with sides 5, 12, and 13 is 30. A perimeter of 90 is 3 x 30 so we multiply the given ratio of the lengths of the triangle by 3 and get 15, 36, and 39. The area is 1/2 base c height = 1/2(36)(15) = 18 x 15 = 270 square units