Chapter 11: Q. 235 (page 1148)

In the following exercises, solve the problem using a system of equations.
The perimeter of a rectangle is 52 cm and its area is 165 cm². Find the length and width of the rectangle.

Short Answer

Expert verified

$(15, 11), (11, 15)$

Step by step solution

Step 1. Given information.

The value of the perimeter of the rectangle is 52 cm and the area is 165 cm²

Step 2. Forming the equations.

Let $l$ be the length and $w$ be the width of the rectangle in cm. Then the perimeter and the area of the rectangle will be $2 (l + w)$ and $l \times w$ , respectively. According to the given conditions,

$2 (l + w) = 52 - - - > (1) l \times w = 165 - - - > (2)$

Step 3. Solving the equations.

Solving equation (2) for l gives

$l = \frac{165}{w}$

Substituting this in equation (1) and then solve it:

$2 (\frac{165}{w} + w) = 52 \frac{165}{w} + w = 26 165 + w^{2} = 26 w [Multiplying both sides by w] w^{2} - 26 w + 165 = 0 w^{2} - 15 w - 11 w + 165 = 0 [Factorizing the equation] (w - 15) (w - 11) = 0$

So, wither $w - 15 = 0$ or $w - 11 = 0$

When $w - 15 = 0$ , then $w = 15$ and from equation (2), $l = \frac{165}{15} = 11$

When $w - 11 = 0$ , then $w = 11$ and from equation (2), $l = \frac{165}{11} = 15$

Hence, as ordered pairs, the solution can be expressed as

$(15, 11), (11, 15)$

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In the following exercises, solve the problem using a system of equations.
The perimeter of a rectangle is 52 cm and its area is 165 cm². Find the length and width of the rectangle.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Forming the equations.

Step 3. Solving the equations.

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In the following exercises, solve the problem using a system of equations.The perimeter of a rectangle is 52 cm and its area is 165 cm2. Find the length and width of the rectangle.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Forming the equations.

Step 3. Solving the equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Probability and Statistics

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the problem using a system of equations.
The perimeter of a rectangle is 52 cm and its area is 165 cm². Find the length and width of the rectangle.