Question

The altitude of triangle is four-third the length of its corresponding base. If the altitude is decreased by 5 cm and the base is increased by 5 cm the area of the triangle would remain the same find the base and altitude of the triangle.​

Answer 1

Answer:

Step-by-step explanation:

Let the length of corresponding base be x.

Thus, altitude will be  

3

5

​  

x.

Now, it is given that altitude is increased by 4 cm i.e.,  

3

5

​  

x+4 and base is decreased by 2 cm i.e., x−2.

The area is same for both.

Therefore,  

2

1

​  

×x×  

3

5

​  

x=  

2

1

​  

×(  

3

5

​  

x+4)×(x−2)

⇒  

3

5

​  

x  

2

=  

3

5

​  

x  

2

−  

3

10

​  

x+4x−8

⇒8=  

3

2

​  

x

⇒x=12

Thus, length of base is 12 cm

and length of altitude is  

3

5

​  

×12=20 cm.