Question

12. A rectangular sheet of cardboard measures 64 cm by 15 cm.

Suppose the width is changed to 16 cm.
What would the length have to be for the rectangle
to have the same area?

Answer 1

To find the length the rectangle would need to be in order to have the same area, divide the original area by the new width.

Step-by-step explanation:

To find the length the rectangle would need to be in order to have the same area, we can use the formula for the area of a rectangle: length x width. The original rectangle has a length of 64 cm and a width of 15 cm, so its area is 64 cm x 15 cm = 960 cm². If we change the width to 16 cm, we need to find the corresponding length that will give us the same area. Let's call this length x. So, the equation becomes: x cm x 16 cm = 960 cm². Solving for x, we divide both sides by 16 cm: x cm = 960 cm² / 16 cm = 60 cm. Therefore, the length would have to be 60 cm for the rectangle to have the same area.

Answer 2

Area of rectangle: length × height

Let the new length be x.

64 × 15 = 16 × x

x = ( 64 × 15 ) ÷ 16

x = 60cm

Why does this work?

It is stated that the area is the same. With that logic, you need to think "I know the area of the rectangular cardboard, so what number multiplied by 16 gives the same area?"

If you check the answer, you will find that 60 × 16 is also
`960 cm^(2)`.