Question

question 9 bcpss_course3_unit6
perry wants to build a railing for the staircase in his home. the height of the staircase is 5 feet, and the horizontal distance from the bottom to the top of the staircase is 12 feet.
what is the length of the railing? enter the answer.
_______ feet
part b
perry wants to extend the horizontal distance to 13 feet with a height of 7 feet. he has enough materials for a 15-foot-long railing. does perry have enough to extend the railing? explain your reasoning. enter the answer.

Explanation:

Step1: Apply Pythagorean theorem (Part A)

The railing is the hypotenuse of a right triangle. For right triangles, $c = \sqrt{a^2 + b^2}$, where $a=12$, $b=5$.
$\text{Length} = \sqrt{12^2 + 5^2}$

Step2: Calculate values (Part A)

Compute squares first, then sum, then root.
$\sqrt{144 + 25} = \sqrt{169} = 13$

Step3: Apply Pythagorean theorem (Part B)

New dimensions: $a=13$, $b=7$.
$\text{New Length} = \sqrt{13^2 + 7^2}$

Step4: Calculate values (Part B)

Compute squares, sum, and root.
$\sqrt{169 + 49} = \sqrt{218} \approx 14.76$

Answer:

Part A: 13 feet
Part B: Yes, Perry has enough materials. The length of the extended railing is approximately 14.76 feet, which is less than the 15 feet of materials he has.