Question

A rectangle is 32m by 8m is similar to a rectangle 4m by x m. Find the 2 possible values of x .

Answer 1

Answers:

x = 1 or x = 16

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Work Shown:

Draw out a rectangle that is 32 units wide horizontally and 8 units tall vertically.

Then draw out another rectangle that is 4 meters wide horizontally and x meters tall vertically.

The horizontal and vertical sides pair up to form these fractions: 32/4 and 8/x

Set the fractions equal to one another. Solve for x

32/4 = 8/x

32x = 8*4 ... cross multiply

32x = 32  

x = 32/32 ... divide both sides by 32

x = 1

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Somewhere else on your paper, draw the same 32 by 8 rectangle to make 32 the horizontal component

Next to this rectangle, draw a rectangle that has x as the horizontal part and 4 as the vertical. Note the swap here.

We now have this equation to solve for

32/x = 8/4

once again, note the swap

Let's solve for x

32/x = 8/4

32*4 = 8*x

128 = 8x

8x = 128

x = 128/8

x = 16