Question

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 a height that is
doubled. Find the difference between the area of the original triangle
and the area of the new triangle.

Answer 1

Answer:

The difference between the area of the original triangle and the area of the new triangle is $\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)$.

Step-by-step explanation:

The equation for the area of a triangle ($A_{\bigtriangleup}$) is:

$A_{\bigtriangleup} = \frac{1}{2}\cdot b \cdot h$

Where:

$b$ - Base, dimensionless.

$h$ - Height, dimensionless.

The expression for each triangle are described below:

First Triangle ($b = 3\cdot x + 7$, $h = 5\cdot x - 1$)

$A_{\bigtriangleup,1} = \frac{1}{2}\cdot (3\cdot x+7)\cdot (5\cdot x -1)$

Second Triangle ($b = 3\cdot (3\cdot x+7)$, $h = 2\cdot (5\cdot x -1)$)

$A_{\bigtriangleup,2} = 3\cdot (3\cdot x+7)\cdot (5\cdot x -1)$

The difference between the area of the original triangle and the area of the new triangle is:

$\Delta A_{\bigtriangleup} = A_{\bigtriangleup,2}-A_{\bigtriangleup,1}$

$\Delta A_{\bigtriangleup} = 3\cdot (3\cdot x+7)\cdot (5\cdot x-1)-\frac{1}{2} \cdot (3\cdot x+7)\cdot (5\cdot x-1)$

$\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)$

The difference between the area of the original triangle and the area of the new triangle is $\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)$.