Question

the altitude of a triangle is 2/3 of its corresponding base. if tge altitude is increased by 4 cm and the base decreased by 2 cm,the area of the triangle remains the same. find the base and the altitude of the triangle

Answer 1

Let the altitude of the trainable be x and the corresponding base be y
The area of the triangle will be 1/2 xy

2/3x=y
So, 2x=3y

So, 1/2 ( x+4)(y-2)= 1/2 xy
1/2xy = 1/2[xy-2x+4y-8]
xy=xy-2x+4y-8
0=-2x+4y-8
2x-4y=(-8)

Now 2x=3y
So ,3y-4y=(-8)
-y=(-8)
y=8

2x=3y
2x=3×8
x=24/2
x=12

Answer:-. The altitude of triangle=x=12cm
The corresponding base of the triangle=y=8cm

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