Question

Lin has a square bedroom. Her sister Tasneem has a room that is 1 m shorter in length than Lin's room,

but 1 m wider.
a. Show that Lin has the larger bedroom.
b. Determine how much bigger Lin's bedroom is than Tasneem's bedroom.

Answer 1

Okay, let's think through this step-by-step:

* Lin has a square bedroom

* Let's define the length of Lin's room as x m

* So Lin's room is x m x x m

* Tasneem's room is 1 m shorter, so its length is (x - 1) m

* Tasneem's room is 1 m wider, so its width is (x + 1) m

a) To show Lin's room is larger:

* Lin's area = x * x = x^2

* Tasneem's area = (x - 1) * (x + 1) = x^2 - 1

* Since x^2 > x^2 - 1, Lin's area is greater.

b) To find the difference:

* Lin's area = x^2

* Tasneem's area = x^2 - 1

* Difference = Lin's area - Tasneem's area

= x^2 - (x^2 - 1)

= 1 m^2

Therefore, Lin's bedroom is 1 m^2 larger than Tasneem's bedroom. By defining the length as a variable x, I avoided picking arbitrary values and showed the relationship between the areas algebraically. This demonstrates Lin's room is larger for any value of x.