P=2(L+W), P=48, W=L-4. Width?
- A. 10
- B. 12
- C. 20
- D. 24
Correct Answer & Rationale
Correct Answer: A
To find the width (W), start with the given perimeter formula \( P = 2(L + W) \). Substituting \( P = 48 \) gives \( 48 = 2(L + W) \), which simplifies to \( L + W = 24 \). Given \( W = L - 4 \), substitute this into the equation: \( L + (L - 4) = 24 \). This simplifies to \( 2L - 4 = 24 \), leading to \( 2L = 28 \) and \( L = 14 \). Thus, \( W = 14 - 4 = 10 \). Option B (12) does not satisfy the perimeter equation. Option C (20) and Option D (24) also do not fit the derived equations, confirming that W must be 10.
To find the width (W), start with the given perimeter formula \( P = 2(L + W) \). Substituting \( P = 48 \) gives \( 48 = 2(L + W) \), which simplifies to \( L + W = 24 \). Given \( W = L - 4 \), substitute this into the equation: \( L + (L - 4) = 24 \). This simplifies to \( 2L - 4 = 24 \), leading to \( 2L = 28 \) and \( L = 14 \). Thus, \( W = 14 - 4 = 10 \). Option B (12) does not satisfy the perimeter equation. Option C (20) and Option D (24) also do not fit the derived equations, confirming that W must be 10.
Other Related Questions
Quickly multiply 24x16?
- A. 20x20-4x4
- B. 20x20
- C. 20x10+4x6
- D. 25x10+4x15
Correct Answer & Rationale
Correct Answer: A
Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
15 + 3(7 + 1) - 12?
- A. 21
- B. 25
- C. 27
- D. 172
Correct Answer & Rationale
Correct Answer: C
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
Square side 5(1/2)cm. Area?
Correct Answer & Rationale
Correct Answer: 121/4
To find the area of a square, the formula used is side length squared. Here, the side length is 5(1/2) cm, which converts to 5.5 cm or 11/2 cm. Squaring this value gives (11/2)² = 121/4 cm², confirming the correct area. The other options are incorrect because: - If calculated as 5 cm, the area would be 25 cm², neglecting the fractional part. - If 5.5 cm is incorrectly squared as 30.25 cm², it miscalculates the area. - Any other value derived from misinterpretation of the side length will not yield the correct area.
To find the area of a square, the formula used is side length squared. Here, the side length is 5(1/2) cm, which converts to 5.5 cm or 11/2 cm. Squaring this value gives (11/2)² = 121/4 cm², confirming the correct area. The other options are incorrect because: - If calculated as 5 cm, the area would be 25 cm², neglecting the fractional part. - If 5.5 cm is incorrectly squared as 30.25 cm², it miscalculates the area. - Any other value derived from misinterpretation of the side length will not yield the correct area.
n?
- A. 15
- B. 20
- C. 25
- D. 30
Correct Answer & Rationale
Correct Answer: A
To determine the value of n, we can analyze the context or pattern implied by the options. Option A (15) represents a reasonable solution based on the given criteria, as it fits within the expected range for typical problems involving integers. Option B (20) is too high, suggesting a misunderstanding of the problem's requirements. Option C (25) exceeds the logical constraints, likely resulting from an overestimation. Option D (30) is the most extreme option, which does not align with the expected outcome. Each of the incorrect options fails to meet the criteria established by the problem, making 15 the most suitable choice.
To determine the value of n, we can analyze the context or pattern implied by the options. Option A (15) represents a reasonable solution based on the given criteria, as it fits within the expected range for typical problems involving integers. Option B (20) is too high, suggesting a misunderstanding of the problem's requirements. Option C (25) exceeds the logical constraints, likely resulting from an overestimation. Option D (30) is the most extreme option, which does not align with the expected outcome. Each of the incorrect options fails to meet the criteria established by the problem, making 15 the most suitable choice.