Question

The altitude of a triangle is three fifth of the length of the corresponding base. If the altitude is decreased by 4cm and the corresponding base is increased by 10 cm, the area of the triangle remain same. Find the base and altitude of the triangle ​

Answer 1

Answer:

LET THE BASE BE X

ALTITUDE Y

1/2 *X*Y=AREA OF Δ

1/2*X*3X/5=AREA OF Δ

1/2*(X+10)*Y-4=AREA

1/2*(X+10)*3X/5-4=AREA

1/2*(X+10)*3X-20/5=AREA

⇒1/2*X*3X/5=1/2*(X+10)*3X-20/5

Solving, we get, X = 40 CM

So, the altitude of the original triangle = 3 x 40/5 cm

                                                             = 24 cm

Hence, the altitude of the original triangle was 24 cm.

Step-by-step explanation: