Question

question 11 | bcpss_course3_unit6
blake is building a model of a bridge out of wood, as shown in the figure. he needs to cut a piece of wood for one of the vertical support beams. what length should he cut? choose the correct answer.
6.5 in.
x in.
6 in.
8.8 inches
3 inches
2.5 inches
0.5 inch

Explanation:

Step1: Identify right triangle sides

The triangle has hypotenuse $c=6.5$ in, one leg $a=6$ in, unknown leg $x$.

Step2: Apply Pythagorean theorem

$$a^2 + x^2 = c^2$$
$$6^2 + x^2 = 6.5^2$$

Step3: Calculate squared values

$$36 + x^2 = 42.25$$

Step4: Solve for $x^2$

$$x^2 = 42.25 - 36 = 6.25$$

Step5: Find square root of $x^2$

$$x = \sqrt{6.25} = 2.5$$

Answer:

2.5 inches