Question

Manny wants to proportionally enlarge a rectangular window that has a length of 36 inches and a width of 24.5 inches.

Answer 1

The new width of the window should be 36.75 inches ⇒ 2nd answer

Step-by-step explanation:

The proportionally is two quantities having a constant ratio

The quantities y and x are proportional if:

• $\frac{y}{x}$ = k, where k is the constant of proportionality
• y = k x
• $\frac{y_{1}}{x_{1}}=\frac{y_{2}}{x_{2}}$

∵ Manny wants to proportionally enlarge a rectangular window

- That means the new dimensions are proportion with the

  original dimensions

∴ New dimensions = k × original dimensions

- k is the constant of proportionally

∵ The original length = 36 inches

∵ The new length = 54 inches

- Substitute then in the equation above to find k

∵ 54 = k × 36

- divide both sides by 36

∴ 1.5 = k

∴ The new dimensions = 1.5 × original dimensions

∵ the original width = 24.5 inches

∴ The new width = 1.5 × 24.5 = 36.75 inches

The new width of the window should be 36.75 inches

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