Question

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?

Answer 1

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

Answer 2

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:


`( L_(1) )/( L_(2) ) = ( W_(1) )/( W_(2) )`
So let's plug it all in from above:


`( 3 )/( L_(2) ) = ( 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)`


`(30)/(5) = ( 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