An altitude of a triangle is 5/3rd the length of its corresponding bas

1.	An altitude of a triangle is 5/3rd the length of its corresponding base. if the altitude is increased by 8 and base is decreased by 4 the area of triangle would remain same. Find the base and altitude of triangle. Hint(Chapter: linear equation in one veriable)
Answer» 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.

An altitude of a triangle is 5/3rd the length of its corresponding base. if the altitude is increased by 8 and base is decreased by 4 the area of triangle would remain same. Find the base and altitude of triangle. Hint(Chapter: linear equation in one veriable)

Answer»

Answer:

LET the length of CORRESPONDING base be x.

Thus, altitude will be

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

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

The area is same for both.

Therefore,

×x×

×(

x+4)×(x−2)

⇒

−

x+4x−8

⇒8=

⇒x=12

Thus, length of base is 12 cm

and length of altitude is

×12=20 cm.