The dimensions of an 8-foot by 12-foot bridge support need to be tripled to create a revised bridge design. Which formulas can be used to determine the area of the new frame? Select all that apply.
[tex]$3^2=\frac{x}{96}$[/tex]
[tex]$A=8 \times 12$[/tex]
[tex]$A=(3 \times 8)(3 \times 12)$[/tex]
[tex]$3^2=\frac{96}{x}$[/tex]
Answer (1)
Calculate the original area: A or i g ina l = 8 × 12 = 96 .
Triple the dimensions: New length = 3 × 12 = 36 , New width = 3 × 8 = 24 .
Calculate the new area: A n e w = 24 × 36 = 864 .
Identify correct formulas: 3 2 = 96 x and A = ( 3 × 8 ) ( 3 × 12 ) .
Explanation
Problem Analysis Let's analyze the problem. We have a bridge support with dimensions 8 feet by 12 feet. The dimensions are tripled to create a new design. We need to find the formulas that can be used to determine the area of the new frame.
Original Area First, let's calculate the area of the original bridge support: A or i g ina l = 8 × 12 = 96 square feet
New Dimensions Next, let's find the dimensions of the new bridge support by tripling the original dimensions: New length = 3 × 12 = 36 feet New width = 3 × 8 = 24 feet
New Area Now, let's calculate the area of the new bridge support: A n e w = ( 3 × 8 ) × ( 3 × 12 ) = 24 × 36 = 864 square feet
Checking Formulas Now, let's check the given formulas:
3 2 = 96 x => 9 = 96 x => x = 9 × 96 = 864 . This formula correctly calculates the new area.
A = 8 × 12 = 96 . This formula calculates the area of the original bridge support, not the new one.
A = ( 3 × 8 ) ( 3 × 12 ) . This formula correctly calculates the new area as we showed above.
3 2 = x 96 => 9 = x 96 => x = 9 96 = 3 32 ≈ 10.67 . This formula does not calculate the new area.
Final Answer Therefore, the formulas that can be used to determine the area of the new frame are: 3 2 = 96 x A = ( 3 × 8 ) ( 3 × 12 )
Examples
When scaling up architectural designs, such as for bridges or buildings, understanding how dimensions affect area is crucial. For instance, if you're designing a park and want to triple the size of a rectangular flower bed that was initially 5 meters by 3 meters, you need to calculate the new area to determine the amount of soil and plants required. The new dimensions would be 15 meters by 9 meters, and the new area would be 135 square meters, nine times the original area. This scaling principle applies to various fields, including urban planning, interior design, and even creating scaled models.
