Question

The perimeter of a rectangle is 112 cm and its breadth is x cm. (i) Find, in terms of x, an expression for the length of the rectangle. (ii) Given that the area of the rectangle is 597 〖cm〗^2, formulate an equation in x and show that it reduces to x^2 – 56x + 597 = 0. (iii) Solve the equation x^2 – 56x + 597 = 0, giving both answers correct to 2 decimal places. (iv) Hence, find the length of the diagonal of the rectangle.

Answer 1

Answer:

The length of rectangle = 40 cm and

The breadth of rectangle = 16 cm

Step-by-step explanation:

Given,

The perimeter of rectangle = 112 cm

Let the length of rectangle = x and

The breadth of rectangle =

To find, the length and breadth of rectangle = ?

We know that,

The perimeter of rectangle = 2(l + b)

∴ 2(x + ) = 112

⇒ x + =

⇒

⇒

⇒ 3x = 60 × 2 = 120

⇒ x =

∴ The length of rectangle = 40 cm and

The breadth of rectangle = = 16 cm

Answer 2

Answer:

➡️Perimeter of a rectangle =2(length +breadth)

(i)Given

perimeter =112cm,breadth=x cm

length=(perimeter/2)-breadth

length=56-x cms

(ii)➡️Area of a rectangle =length×bredth

so x(56-x)=597

=>x^2-56x+597=0

(iii)x=14.325,41.675

(iv)length=14.325 or 41.675cm

$diagonal = \sqrt{ {length}^{2} + {breadth}^{2} }$

so diagonal=44.02cm