Question

One side of a rectangle is three times as long as another. If its area is 363 square centimeters, find its dimensions.

Answer 1

9514 1404 393

Answer:

  11 cm by 33 cm

Step-by-step explanation:

You can solve this problem mentally as follows.

Consider the rectangle as 3 squares, side-by-side. Then the area of each of those squares is 363/3 = 121 cm^2. From your knowledge of the squares of numbers, you know that 121 = 11^2. So, the width of the rectangle is 11 cm, and the length is 3 times that, or 33 cm.

_____

Using variables, we can let w represent the width. Then 3w can represent the length, and the area is ...

  A = LW

  A = (3w)(w) = 3x^2 = 363

  w^2 = 363/3 = 121

  w = √121 = 11

  3w = 3·11 = 33

The width is 11 cm; the length is 33 cm.

Answer 2

Answer:

Shorter side: 11 cm

Longer side: 33 cm

First, write down what you know:

length=3*width, this can be written as 3w

area=363 sq cm

Now we know the formula for the area of a rectangle= length * width so we can substitute what we know into the formula. It looks like this:

        363 (area) = 3w (length) × w (width)

        $363=w^2$

  divide both sides by 3 to get: 121 = $w^2$

   take the square root of both sides to get: w=11 (square root of 121 is 11)

Now that we know what the width is, we can substitute that and find the length: 3w = 3 × 11=33

So length (longer side) is 33cm and width (shorter side) is 11cm.

*To check this, plug the numbers into the area formula: Area=33 × 11 = 363 sq cm.

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