Chapter 7: Q16. (page 463)

MULTIPLE CHOICE Antonia is carpeting two of the rooms in her house. The dimensions are shown. What is the total area to be carpeted?
F $x^{2} + 3 x$
G $2 x^{2} + 6 x - 10$
H $x^{2} + 3 x - 5$
J $8 x + 12$

Short Answer

Expert verified

The total area to be carpeted is $2 x^{2} + 6 x - 10$ .

Step by step solution

Step 1. Write formula of area of rectangle.

Area of rectangle is given by $A = length (l) \times breadth (b)$ .

Step 2. Find the area of first room.

Replace $l$ with $x + 3$ and b with x, in $A = length (l) \times breadth (b)$ .

$A_{1} = (x + 3) x = x^{2} + 3 x$

Step 3. Find the area of second room.

Replace $l$ with $x + 5$ and b with $x - 2$ , in $A = length (l) \times breadth (b)$ .

$A_{2} = (x + 5) (x - 2) = x (x - 2) + 5 (x - 2) = x^{2} - 2 x + 5 x - 10 = x^{2} + 3 x - 10$

Step 4. Find the total area.

To find the total area, add $A_{1}$ and $A_{2}$ .

$A_{1} + A_{2} = (x^{2} + 3 x) + (x^{2} + 3 x - 10) = 2 x^{2} + 6 x - 10$

Therefore, the total area to be carpeted is $2 x^{2} + 6 x - 10$ . As the obtained area completely matches with option G. Therefore, option G is the correct answer.

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Planet	Distance from Sun (km)
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MULTIPLE CHOICE Antonia is carpeting two of the rooms in her house. The dimensions are shown. What is the total area to be carpeted?
F $x^{2} + 3 x$
G $2 x^{2} + 6 x - 10$
H $x^{2} + 3 x - 5$
J $8 x + 12$

Short Answer

Step by step solution

Step 1. Write formula of area of rectangle.

Step 2. Find the area of first room.

Step 3. Find the area of second room.

Step 4. Find the total area.

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MULTIPLE CHOICE Antonia is carpeting two of the rooms in her house. The dimensions are shown. What is the total area to be carpeted?Fx2+3xG2x2+6x−10Hx2+3x−5J8x+12

Short Answer

Step by step solution

Step 1. Write formula of area of rectangle.

Step 2. Find the area of first room.

Step 3. Find the area of second room.

Step 4. Find the total area.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

MULTIPLE CHOICE Antonia is carpeting two of the rooms in her house. The dimensions are shown. What is the total area to be carpeted?
F $x^{2} + 3 x$
G $2 x^{2} + 6 x - 10$
H $x^{2} + 3 x - 5$
J $8 x + 12$