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Bilal is assembling a set of bunkbeds and wants to make sure the support posts are perpendicular to the floor. He measures that the posts are 165 centimeters (cm) tall and 220cm apart. How long should the diagonal measurement be, in cm, if the support posts are perpendicular to the floor? Choose 1 answer: (A) 75 (B) 130 (C) 275 (D) 385

Bilal is assembling a set of bunkbeds and wants to make sure the support posts are perpendicular to the floor. He measures that the posts are 165165 centimeters (cm) (\mathrm{cm}) tall and 220 cm 220 \mathrm{~cm} apart. How long should the diagonal measurement be, in cm \mathrm{cm} , if the support posts are perpendicular to the floor?\newlineChoose 11 answer:\newline(A) 7575\newline(B) 130130 \newline(C) 275275\newline(D) 385385

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Q. Bilal is assembling a set of bunkbeds and wants to make sure the support posts are perpendicular to the floor. He measures that the posts are 165165 centimeters (cm) (\mathrm{cm}) tall and 220 cm 220 \mathrm{~cm} apart. How long should the diagonal measurement be, in cm \mathrm{cm} , if the support posts are perpendicular to the floor?\newlineChoose 11 answer:\newline(A) 7575\newline(B) 130130 \newline(C) 275275\newline(D) 385385
  1. Identify Relationship and Triangle: Identify the relationship between the height of the posts, the distance apart, and the diagonal measurement.\newlineThe posts and the floor form a right-angled triangle, with the posts as one side, the distance between the posts as the base, and the diagonal as the hypotenuse. We can use the Pythagorean theorem to find the length of the diagonal (hypotenuse).
  2. Apply Pythagorean Theorem: Apply the Pythagorean theorem.\newlineThe Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (cc) is equal to the sum of the squares of the other two sides (aa and bb). The formula is c2=a2+b2c^2 = a^2 + b^2.
  3. Plug in Known Values: Plug in the known values into the Pythagorean theorem.\newlineLet's denote the height of the posts as 'aa' (165165 cm), the distance apart as 'bb' (220220 cm), and the diagonal as 'cc'. So we have:\newlinec2=a2+b2c^2 = a^2 + b^2\newlinec2=1652+2202c^2 = 165^2 + 220^2
  4. Calculate Squares: Calculate the squares of the given numbers.\newline1652=27225165^2 = 27225\newline2202=48400220^2 = 48400
  5. Add Squares: Add the squares of the two sides.\newlinec2=27225+48400c^2 = 27225 + 48400\newlinec2=75625c^2 = 75625
  6. Find Square Root: Find the square root of the sum to get the length of the diagonal. \newlinec=75625c = \sqrt{75625}\newlinec=275c = 275
  7. Match with Given Options: Match the calculated diagonal length with the given options.\newlineThe calculated diagonal length is 275 cm275\,\text{cm}, which corresponds to option (C).

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