Triangles

Geometry Level 4

If the altitudes of a triangle are in the ratio 15 : 21 : 35 15:21:35 then ratio of their corresponding sides is __________ \text{\_\_\_\_\_\_\_\_\_\_} .

3 : 5 : 7 3:5:7 7 : 5 : 3 7:5:3 4 : 5 : 6 4:5:6 15 : 21 : 35 15:21:35 35 : 21 : 15 35:21:15

Anshu Garg by anshu garg , 18, India

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1 solution

There is only 1 triangle .

We know that the area of any triangle = 1/2 * b * h

If we take the heights as h1= 15x , h2 = 21x and h3 = 35x and the bases corresponding to them be a , b and c respectively.

Then , Ar. triangle = 1/2* h1* a = 1/2* h2* b = 1/2* h3 * c 

                         =>  1/2* 15x* a = 1/2* 21x* b = 1/2* 35x* c

                         =>   15a = 21b = 35c

                         =>   a = 7/5 b and c = 3/5 b

                          a : b : c 

                    = 7/5b : b : 3/5b

                    = 7 : 5 : 3
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