A rectangle of length L and width W and a square of side x have equal perimeters. The length L is 10 more than x. Express W in terms of x.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

A rectangle of length L and width W has a perimeter of 2(L + W). A square with side of length x has a perimeter of 4x.

Here we have the perimeter of a rectangle with length L and width W equal to the perimeter with side x and L is 10 more than x.

This gives 2(L + W) = 4x

as L = 10 + x

=> 2(10 + x + W) = 4x

=> 10 + x + W = 2x

=> W = x - 10

The width of the rectangle in terms of x is W = x - 10.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write the perimeter of the rectangle:

P1 = 2(L+W)

We'll write the perimeter of the square:

P2  = 4x

We know that P1 = P2 => 2(L+W) = 4x => (L+W) = 2x

We also know that L = 10+x

10+x+W = 2x

We'll isolate W to the left side:

W = 2x - x - 10

W = x - 10

The width W expressed in terms of x is: W = x - 10.

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