A triangle has a base of (3x+7) and a height of (5x-1)a second triangle is drawn with a base that is tripled and its height is doubled. Find the difference between the area of the original triangle and the area of the new triangle

The difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

Step-by-step explanation:

We know that the area of a triangle A = 1/2bh where b = base and h = height.

Let A be the area of triangle 1 with base (3x + 7) and height (5x - 1).

So its area A = (3x + 7)(5x - 1)/2.

Now for the second triangle, the base is tripled, so its base is 3(3x + 7) and its height is doubled, so its height is 2(5x - 1)

So its area is A' = 3(3x + 7) × 2(5x - 1)/2 = 3(3x + 7)(5x - 1)

So the difference between the area of the original triangle and the new triangle is

A' - A = 3(3x + 7)(5x - 1) - (3x + 7)(5x - 1)/2

= (3x + 7)(5x - 1)(3 - 1/2)

= 5(3x + 7)(5x - 1)/2

So the difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

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step-by-step explanation:

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction