Question

The length of a rectangle
is 3cm more than
thrice its breath. Its diagonal is 1cm more than
the length. What are the length and breath of the
rectangle?
(Let the breath=x and length= 3x+3)​

Answer 1

Answer:

Here, Alpha= 3+√14 and beta= 3-√14

Step-by-step explanation:

• √14= 3.742

• It means that beta= 3-3.742 = -0.742(as it is length so it cannot be negative).

Now, alpha = 3+3.742=6.742

i.e. x= 6.742 ..

So, breadth of rectangle is 6.742cm and length of rectangle is [(3×6.742) +3] = 20.226+3= 23.226cm

Answer 2

Given :-

• The length of a rectangle is 3cm more than thrice its breath. Its diagonal is 1cm more than the length.

To Find :-

• Length of rectangle = ?
• Breadth of rectangle = ?

Solution :-

• Let Breadth be x , then Length will be 3x + 3 and digonal will be 3x + 4

• We know that,each angle of rectangle is 90°.

Now,By Phythagoras theorem we get :

• (Hypotenuse)² = (Perpendicular)² + (Base)²

Where,

• Hypotenuse = 3x + 4
• Perpendicular = x
• Base = 3x + 3

→ (3x + 4)² = (x)² + (3x + 3)²

By using algebric Identity : (a + b)² = a² + b² + 2ab we get :

→ 3x² + 4² + 2(3x) (4) = x² + 3x² + 3² + 2(3x)(3)

→ 3x² + 16 + 24x = 4x² + 9 + 18x

Combining like terms we get :

→ 16 - 9 + 24x - 18x = 4x² - 3x²

→ 7 + 6x = x²

→ x² - 6x - 7 = 0

By using splitting middle term we get :

→ x² - 7x + x - 7

→ x(x - 7) + 1(x - 7)

→ (x + 1) (x - 7)

→ x = -1 or 7

• Ignoring the negative value beacuse Breadth cannot be negative

→ x = 7

Therefore,

• Length of rectangle = 3x + 3 = 3(7) + 3 = 21 + 3 = 24 cm
• Breadth of rectangle = x = 7 cm