Question

Carpenters use a tool called a speed square to help them mark right angles . A speed square is a right triangle

Answer 1

Answer:

A. $Area = \frac{1}{2}(2x^2 - 2x - 24)$

B. $Area = 3.75 in^2$

Step-by-step explanation:

A. $Area = \frac{1}{2}bh$

Where,

$b = 2x + 6$

$h = x - 4$

Plug in the values to get a polynomial that represents the area of the tool

$Area = \frac{1}{2}(2x + 6)(x - 4)$

$Area = \frac{1}{2}(2x(x - 4) + 6(x - 4)$

$Area = \frac{1}{2}(2x^2 - 8x + 6x - 24)$

$Area = \frac{1}{2}(2x^2 - 2x - 24)$

B. To find area, when x = 4.5 in, plug in the value of x into the equation for the area of the tool.

$Area = \frac{1}{2}(2(4.5)2 - 2(4.5) - 24)$

$Area = \frac{1}{2}(2(20.25) - 9 - 24)$

$Area = \frac{1}{2}(40.5 - 9 - 24)$

$Area = \frac{1}{2}(7.5)$

$Area = 3.75 in^2$