A rectangle has a length of 8 units and a width of 6 units. Which of the following stateme… — GRE General Test

A rectangle has a length of $8$ units and a width of $6$ units. Which of the following statements about this rectangle must be true? Select all that apply.

The area of the rectangle is $48$ square units.Answer
The length of each diagonal of the rectangle is $10$ units.Answer
The perimeter of the rectangle is $28$ units.Answer
D
The length of each diagonal of the rectangle is $14$ units.
E
The area of the rectangle is $28$ square units.

Answer

The correct statements are that the area of the rectangle is 48 square units, the length of each diagonal is 10 units, and the perimeter of the rectangle is 28 units.

The statement regarding the area being 48 square units is correct because

8 \times 6 = 48

. The statement regarding the diagonal being 10 units is correct because

\sqrt{8^2 + 6^2} = 10

. The statement regarding the perimeter being 28 units is correct because

2 \times (8 + 6) = 28

Step-by-Step Solution

Calculate the area of the rectangle

\text{Area} = 8 \times 6 = 48

square units

The area formula for a rectangle is length multiplied by width.

Calculate the length of the diagonal using the Pythagorean theorem

\text{Diagonal} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = 10

units

The sides and diagonal of a rectangle form a right triangle where the diagonal is the hypotenuse.

Calculate the perimeter of the rectangle

\text{Perimeter} = 2 \times (8 + 6) = 28

units

The perimeter formula for a rectangle is twice the sum of its length and width.

Key Concept

Basic geometric properties of rectangles including area, perimeter, and diagonal calculation via the Pythagorean theorem.

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Step-by-Step Solution

Key Concept

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