Question

An altitude of a triangle is 5 times the length of its corresponding base. If the altitude is increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains unchanged find the base and the altitude.


pls help me​

Answer 1

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.

Answer 2

Answer:

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