Chapter 11: Q. 79 (page 774)

The perimeter of a rectangle is $16$ inches, and its area is $15 i n c h e s^{2}$ . What are its dimensions?

Short Answer

Expert verified

The dimensions are $5 i n c h e s b y 3 i n c h e s$ .

Step by step solution

Step 1. Given information.

Assume the length and breadth of the rectangle is l and b.

From the question,

$2 (l + b) = 16 . . . . . . (i) l \times b = 15 . . . . . . (i i)$

Solve equation (ii) for l,

$l = \frac{15}{b}$

Substitute the value of l in equation (i),

role="math" localid="1646842713350" $2 (\frac{15}{b} + b) = 16 \frac{15 + b^{2}}{b} = 8 15 + b^{2} - 8 b = 0 . . . . . . (i i i)$

Step 2. Factor equation (iii).

On factoring equation (iii), we get,

$(b - 3) (b - 5) = 0 b = 3, 5$

Substitute $b = 3$ in equation (ii),

$l \times (3) = 15 l = 5$

Substitute $b = 5$ in equation (ii),

$l \times (5) = 15 l = 3$

Therefore, the dimension are role="math" localid="1646842885426" $5 i n c h e s b y 3 i n c h e s$ .

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The perimeter of a rectangle is $16$ inches, and its area is $15 i n c h e s^{2}$ . What are its dimensions?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor equation (iii).

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The perimeter of a rectangle is 16inches, and its area is 15inches2. What are its dimensions?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor equation (iii).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

The perimeter of a rectangle is $16$ inches, and its area is $15 i n c h e s^{2}$ . What are its dimensions?