Question

Help me do my question

Answer 1

Note:

`\text{Area of rectangle = Length of rectangle }* \text{ breadth of rectangle}\\\\\therefore\ \text{Length of rectangle }=\frac{\text{Area of rectangle }}{\text{Breadth of rectangle}}\\\\\text{Similarly, breadth of rectangle = }\frac{\text{Area of rectangle }}{\text{Length of rectangle}}`

Answer:

`4\text{cm}`

Explanation:

`\text{(1) Breadth of green rectangle }=\frac{\text{Area of green rectangle}}{\text{Length of green rectangle}}=(12)/(4)=3\text{cm}`

`\text{(2) Length of yellow rectangle = }\frac{\text{Area of yellow rectangle}}{\text{Breadth of yellow rectangle}}=(9)/(3)=3\text{cm}`

`\text{(3) Length of purple rectangle = Length of (green rectangle + yellow rectangle)}\\\text{or, Length of purple rectangle = 4 + 3 = 7cm}`

`\text{(4) Breadth of purple rectangle = }\frac{\text{Area of purple rectangle }}{\text{Length of purple rectangle}}=(14)/(7)=2\text{cm}`

`\text{(5) Breadth of red rectangle = breadth of (yellow rectangle + purple rectangle)}\\\text{or, Breadth of red rectangle }=3+2=5\text{cm}`

`\text{(6) Length of red rectangle}=\frac{\text{Area of red rectangle}}{\text{Breadth of red rectangle}}=(25)/(5)=5\text{cm}`

`\text{(7) Length of blue rectangle = Length of (red rectangle + purple rectangle)}\\\text{or, Length of blue rectangle = }5+7 =12\text{cm}`

`(8)\ \text{Breadth of blue rectangle = }\frac{\text{Area of blue rectangle}}{\text{Length of blue rectangle }}=(48)/(12)=4\text{cm}`

Answer 2

4 cm

Explanation:

To calculate the area of a rectangle, we find the product of its width and length. This means that to determine the width or length of a rectangle, we can divide the area by the other dimension (length or width) accordingly. Therefore, the formulas are:

`\large\boxed{\begin{array}{l}\textsf{Area\;of\;a\;rectangle}= \sf Length * Width\\\\\textsf{Length of a rectangle}=\sf (Area)/(Width)\\\\\textsf{Width of a rectangle}=\sf (Area)/(Length)\end{array}}`

Note that in a rectangle, the longer side is referred to as "length" and the shorter side as "width".

Starting with the green rectangle, we can calculate its width by dividing its area (12 cm²) by its length (4 cm):

`\sf Width_(green)=(12\;cm^2)/(4\;cm)=3\;cm`

Now we have one side of the yellow rectangle, we can calculate the length of the other side by dividing its area (9 cm²) by 3 cm:

`\sf Length_(yellow)=(9\;cm^2)/(3\;cm)=3\;cm`

(The yellow rectangle is in fact a square, since its length and width are the same).

The length of the purple rectangle is the sum of the lengths of the yellow and green rectangles. Therefore:

`\sf Length_(purple)=3\;cm+4\;cm=7\;cm`

To find the width of the purple rectangle, divide its area (14 cm²) by its length (7 cm):

`\sf Width_(purple)=(14\;cm^2)/(7\;cm)=2\;cm`

The width of the red rectangle is the sum of the widths of the yellow and purple rectangles. Therefore:

`\sf Width_(red)=3\;cm+2\;cm=5\;cm`

To find the length of the red rectangle, divide its area (25 cm²) by its width (5 cm):

`\sf Length_(red)=(25\;cm^2)/(5\;cm)=5\;cm`

(The red rectangle is in fact a square, since its length and width are the same).

The length of the blue rectangle is the sum of the lengths of the red and purple rectangles. Therefore:

`\sf Length_(blue)=5\;cm+7\;cm=12\;cm`

Finally, to find the width of the blue rectangle, divide its area (48 cm²) by its length (12 cm):

`\sf Width_(blue)=(48\;cm^2)/(12\;cm)=4\;cm`

Therefore, the width of the blue rectangle is 4 cm.