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Difficulty: HardTriangles and Pythagorean Theorem

A computer monitor is shaped like a rectangle. It has a diagonal measurement of 2626 inches and a height of 1010 inches. What is the perimeter of the computer monitor?

  1. 6868 inchesAnswer
  2. B
    240240 inches
  3. C
    5252 inches
  4. D
    7272 inches

Answer

The correct perimeter of the monitor is 6868 inches.
The correct answer is found by first recognizing that the diagonal, height, and width form a right triangle. Using the Pythagorean theorem, the missing width is calculated as the square root of (262−10226^2 - 10^2), which equals 2424 inches. The perimeter of the rectangular monitor is then 22 times the height plus 22 times the width: 2(10)+2(24)=682(10) + 2(24) = 68 inches.

Step-by-Step Solution

1
Identify the right triangle formed by the monitor's dimensions.
The diagonal (2626 inches) is the hypotenuse, and the height (1010 inches) is one leg.
A rectangle's diagonal divides it into two identical right triangles.
2
Use the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) to find the missing width.
102+b2=26210^2 + b^2 = 26^2 → 100+b2=676100 + b^2 = 676 → b2=576b^2 = 576 → b=24b = 24 inches.
The width is required to calculate the perimeter of the rectangle.
3
Calculate the perimeter of the rectangle.
P=2l+2w=2(10)+2(24)=20+48=68P = 2l + 2w = 2(10) + 2(24) = 20 + 48 = 68 inches.
The perimeter is the total distance around the outside of the monitor.

Key Concept

Triangles and Pythagorean Theorem
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Topics

Triangles and Pythagorean Theorem

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