A rectangular television screen has a horizontal width of 20\text{ inches} and a vertical … — Armed Services Vocational Aptitude Battery (ASVAB)

A rectangular television screen has a horizontal width of $20\text{ inches}$ and a vertical height of $15\text{ inches}$ . What is the length of the diagonal of the screen?

A
$5\text{ inches}$
B
$\sqrt{175}\text{ inches}$
$25\text{ inches}$ Answer
D
$35\text{ inches}$

Answer

The correct length of the diagonal is

25\text{ inches}

The diagonal of the screen forms the hypotenuse of a right triangle with the width and height acting as the two legs. By applying the Pythagorean theorem (

a^2 + b^2 = c^2

), we calculate

20^2 + 15^2 = 400 + 225 = 625

. Taking the square root of 625 gives a diagonal length of 25 inches.

Step-by-Step Solution

Identify the shape and the relationship between the given measurements.

The width (

20\text{ inches}

) and height (

15\text{ inches}

) form the legs of a right triangle, and the diagonal represents the hypotenuse.

A rectangle's corners are right angles, so drawing a diagonal line creates two identical right triangles.

Apply the Pythagorean theorem (

a^2 + b^2 = c^2

) to find the missing hypotenuse.

15^2 + 20^2 = c^2

The Pythagorean theorem relates the lengths of the legs (

a

and

b

) to the hypotenuse (

c

) in any right triangle.

Square the lengths of the legs and add them together.

225 + 400 = 625

Following the order of operations, exponents must be evaluated before addition.

Take the square root of the sum to find the length of the diagonal.

\sqrt{625} = 25\text{ inches}

To solve for

c

from

c^2

, we must find the principal square root.

Key Concept

Using the Pythagorean theorem to find the hypotenuse (diagonal) of a right triangle formed within a rectangle.

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic