Question

The length and width of a rectangle ABCD are 24 cm and 18 cm respectively. Given that rectangle ABCD is similar to rectangle PQRS. Find (i) the width of rectangle PQRS if its length PQ is 36cm.(ii) the length of rectangle PQRS if its width QR is 36cm.​

Answer 1

Given,

=> Dimensions (rectangle ABCD) = 24 cm,

=> Dimensions (rectangle PQRS) = 36 cm

To find,

=> (i) width (rectangle PQRS) = ?

Solution,

• At first calculate the area of rectangle ABCD, (then calculate the lenght or width of rectangle PQRS)

=> Area (rectangle ABCD) = 1 x B

=> Area (rectangle ABCD) = 24 x 18

=> Area (rectangle ABCD) = 432 cm²

• Now calculate the length or width of rectangle PQRS before calculating its breadth or length we have to notice in the question. In the given question rectangle ABCD is similar to rectangle PQRS.

To find the wide of the rectangle PQRS, if its length is 36 cm.

We have,

• In rectangle PQRS (for calculate wide)

• Length = 36 cm

• Area = 432

=> Wide (rectangle PQRS) = Area/Length

=> = 432/36

=> = 12 cm

To find the length of the rectangle PQRS, if its wide is 36 cm.

We have,

• In rectangle PQRS (for calculate length)

• Wide = 36 cm

• Area = 432

=> Length (rectangle PQRS) = Area/Wide

=> = 432/36

=> = 12 cm

Answer 2

Given:

$\tt{\implies Dimensions\:_{(rectangle\:ABCD)}=24cm\:and\:18cm}⟹Dimensions </p><p>(rectangleABCD)$

$\tt{\implies Dimensions\:_{(rectangle\:PQRS)}=36cm\:and\:xcm}⟹Dimensions </p><p>(rectanglePQRS)$

$\sf\large\underline{To\:Find:}$

$\tt{\implies Width\:_{(rectangle\:PQRS)}=?}⟹Width </p><p>(rectanglePQRS)</p><p>$

$\sf\large\underline{Solution:} </p><p>$

At first calculate the area of rectangle ABCD than calculate the length or width of rectangle PQRS]

$\tt{\implies Area\:_{(rectangle\:ABCD)}=lxb}⟹Area </p><p>(rectangleABCD)$

$\tt{\implies Area\:_{(rectangle\:ABCD)}=24*18}⟹Area$

$\tt{\implies Area\:_{(rectangle\:ABCD)}=432cm^2}⟹Area$

Now calculate the length or width of rectangle PQRS before calculating it's breadth or length w have to notice in the question question. In the given Question rectangle ABCD is similar to rectangle PQRS

To find the wide of rectangle PQRS if it's length is 36cm

We have,

In rectangle PQRS (for calculate wide)

Length=36cm

Area=432

$\tt{\implies wide\:_{(rectangle\:PQRS)}=\dfrac{Area}{length}}⟹wide </p><p>(rectanglePQRS)</p><p> </p><p> = </p><p>length</p><p>Area$

$\tt{\implies wide\:_{(rectangle\:PQRS)}=\dfrac{432}{36}}⟹wide </p><p>(rectanglePQRS)$

$\tt{\implies wide\:_{(rectangle\:PQRS)}=12cm}⟹wide$

To find the length of rectangle PQRS if it's wide is 36cm

We have,

In rectangle PQRS (for calculate wide)

wide=36cm

Area=432

$\tt{\implies Length\:_{(rectangle\:PQRS)}=\dfrac{Area}{wide}}⟹Length </p><p>(rectanglePQRS)</p><p> </p><p> = </p><p>wide</p><p>Area</p><p>$

$\tt{\implies Length\:_{(rectangle\:PQRS)}=\dfrac{432}{36}}⟹Length </p><p>(rectanglePQRS)</p><p> </p><p> = </p><p>36</p><p>432$

$\tt{\implies Length\:_{(rectangle\:PQRS)}=12cm}⟹Length </p><p>(rectanglePQRS)</p><p> </p><p> =12cm$