Question

28) The areas of a square and a rectangle are equal
The length of the rectangle is greater than the
length of any side of the square by 5 cm and
the breadth is less by 3 cm. Find the perimeter
of the rectangle
(a) 17 cm
(b) 26 cm
(C) 30 cm
(d) 34 cm
​

Answer 1

26 cm

Step-by-step explanation:

if answer is correct then mark me as a breainlist

Answer 2

★ Given:

The areas of a square and a rectangle are equal.

The length of the rectangle is greater than the side of the square by 5 cm.

The breadth of the rectangle is less than the side of the square by 3 cm.

★ To Find:

The perimeter of the rectangle.

★ Formulae to be used:

→ $\sf{\boxed{Area\:of\:square=a^2}}$

→ $\sf{\boxed{Area\:of\:rectangle=lb}$

→ $\sf{\boxed{Perimeter\:of\:rectangle=2(l+b)}}$

★ Solution

Let the side of the square be a.

So, length of the rectangle = a + 5

Breadth of the rectangle = a - 3

It is given that the area of the square and the rectangle are equal.

Area of the square = a²

Area of the rectangle = lb

Forming an equation from the statements:

a² = lb

→ Providing the values of the variables.

a² = (a + 5)(a - 3)

→ Distributing the values:

= a² = a x (a - 3) + 5 x (a -3)

= a² = a² - 3a + 5a - 15

→ Combining the like terms:

= a² = a² + 2a - 15

→ Moving the like terms to the LHS:

= a² - a² -2a - 15

= 0 = -2a - 15

→ Moving the constant term to the LHS:

= 15 = 2a

a = 15/2

a = 7.5

Now:

Length of the rectangle = a + 5

= 7.5 + 5

= 12.5 cm

Breadth of the rectangle = a - 3

= 7.5 - 3

= 4.5 cm

Perimeter of rectangle = 2 (l+ b)

= 2 (12.5 + 4.5)

= 2 x 17

= 34 cm

Hence the required correct option is Option D: 34 cm.

Knowledge Bytes:

→ Square

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large x\ cm}\put(4.4,2){\bf\large x\ cm}\end{picture}$

Please refer the first attachment to view the latex figure.

✳ A square is a quadrilateral with all the four sides as equal and parallel. All the angles of a square are right angled.

→ Rectangle

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large x cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large y cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Please refer the second attachment to view the latex figure.

✳ A rectangle is a quadrilateral with the opposite pairs of sides as equal and parallel. All the angles of a rectangle are equal.