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Jamal is making two paintings using canvases that are similar rectangles. The length of the smaller canvas is 3 ft and the width is 5 ft.


What is the length of the larger canvas if the width is 10 ft?

Verified Answer :

ddk

Let's start with what we know:

Smaller canvas:
Length (\(L_{1}\)) = 3ft
Width (\(W_{1}\)) = 5ft

Larger canvas:
Length (\(L_{2}\)) = ?
Width (\(W_{2}\)) = 10ft

Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:

\(\frac{ L_{1} }{ L_{2} } = \frac{ W_{1} }{ W_{2} }\)
So let's plug it all in from above:

\(\frac{ 3 }{ L_{2} } = \frac{ 5 }{ 10 }\)
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:

\((3)(10) = (5)(L_{2})\)
\(30 = 5L_{2}\)
Now divide each side by 5 to isolate \(L_{2}\)

\(\frac{30}{5} = \frac{ 5L_{2}}{5}\)
The 5s on the right cancel out, leaving us with:

\(6 = L_{2}\)

So the length of the larger canvas is 6 ft

johnhrbek

It's not as complicated as you think. The smaller rectangle is 3ft with a width of 5ft. It's asking what the length of the larger canvas is if the width is 10ft. So you pretty much just do 10/5 which is 2 then you multiply 3ft by 2 and you get 6ft.

If you need any help just ask :)

-John

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