Sally is an architect who creates a blueprint of a rectangular dining room. The area of the actual dining room is 1600 times larger than the area of the dining room on the blueprint. The length of the dining room on the blueprint is 3 inches. What is the length of the actual dining room in inches?

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timmyabc19 timmyabc19 · Answer 1 · 2021-03-10T04:52:32+01:00

Answer:

3 times 1600 = 4800

Step-by-step explanation:

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MrRoyal MrRoyal · Answer 2 · 2021-09-10T16:58:43+02:00

Scale ratios are used to show the relationship between objects, where one of the objects is the enlarged version of the other.

The actual length of the dinning room is 120 inches

Given that:

[tex]A_1 \to[/tex] the actual area

[tex]A_2 \to[/tex] area of the blueprint

So, we have:

[tex]A_1: A_2 = 1600 : 1[/tex]

Rewrite as:

[tex]A_1: A_2 = 40 \times 40 : 1 \times 1[/tex]

Apply the formula of area of rectangle

[tex]L1 \times W_1: L_2 \times W_2 = 40 \times 40 : 1 \times 1[/tex]

Given that:

[tex]L_2 = 3[/tex]

The equation becomes

[tex]L1 \times W_1: 3\times W_2 = 40 \times 40 : 1 \times 1[/tex]

Express the ratio as a fraction

[tex]\frac{L1 \times W_1}{3\times W_2} = \frac{40 \times 40}{ 1 \times 1}[/tex]

Split

[tex]\frac{L1 }{3} \times \frac{W_1}{W_2} = \frac{40}{1} \times \frac{40}{ 1}[/tex]

By comparison:

[tex]\frac{L1 }{3}= \frac{40}{1}[/tex]

[tex]\frac{L1 }{3}= 40[/tex]

Multiply both sides by 3

[tex]L_1 = 3 \times 40[/tex]

[tex]L_1 = 120[/tex]

Hence, the actual length of the dinning room is 120 inches