Question

The length and width of a rectangle

added together is 124. If the width is
subtracted from the length it equals 32.
Find the length and width of this rectangle.

Answer 1

The length of rectangle is 78 and width is 46

Explanation:

Let l be the length of rectangle and w be the width of rectangle

Then according to given statement

"The length and width of a rectangle added together is 124"

`l+w = 124` Eqn 1

And

`l-w = 32` Eqn 2

The equation form a system of linear equation in two variables. We can use different methods to solve he system.

We will use the elimination method

Adding equation 1 and equation 2

`l+w+l-w = 124+32\\2l = 156\\(2l)/(2) = (156)/(2)\\l = 78`

Putting l = 78 in equation 1

`78+w = 124\\w = 124-78\\w = 46`

Hence,

The length of rectangle is 78 and width is 46