Question

The length of a rectangle is 3 cm more than thrice its breath.Its diagonal is 1 cm more than the length. what are the length and breath of the rectangle?​

Answer 1

✬ Length = 24 cm ✬

✬ Breadth = 7 cm ✬

Step-by-step explanation:

Given:

• Length of rectangle is 3 cm more than thrice the breadth.
• Diagonal is 1 cm more than length.

To Find:

• What are the length & breadth ?

Solution: Let the breadth of rectangle be x cm. Therefore,

➟ Thrice of breadth = 3x cm

• Length = 3 more than 3x = 3x + 3

• Diagonal = 1 more than length = 3x + 4

We know that the each angle of a rectangle is of 90°. Let's consider in rectangle ABCD

• BC = length
• AB = breadth
• AC = diagonal
• ∠ABC = 90°

Now consider the right angled ∆ABC , we have

• AB {perpendicular}
• BC {base}
• AC {hypotenuse}

Using Pythagoras theorem

★ H² = Perpendicular² + Base² ★

➮ (3x + 4)² = x² + (3x + 3)²

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

➮ 9x² + 16 + 24x = x² + 9x² + 9 + 18x

➮ 16 – 9 + 24x = x² + 18x

➮ 7 + 24x – 18x = x²

➮ 7 + 6x = x²

➮ 0 = x² – 6x – 7

Using middle term splitting method.

➮ x² + x – 7x – 7

➮ x(x + 1) – 7 (x + 1)

➮ (x + 1) (x – 7)

➮ x = –1 or x = 7

• We will take positive because length cannot be negative.

So,

• Breadth = x = 7 cm
• Length = 3(7) + 3 = 24 cm
• Diagonal = 3(7) + 4 = 25

Answer 2

Answer :-

• Breadth = 7cm
• Length = 24cm

Given :-

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

To Find :-

• Length and breadth of the rectangle.

Solution :-

Let

• Breadth = x
• Length will be 3x + 3
• Diagonal will be 3x + 4

As we know that

each angle of a rectangle is of 90°

Here

• Perpendicular = x
• base = 3x + 3
• hypotenuse = 3x + 4

As we know that

h² = p² + b²

Now,

(3x + 4)² = (x)² + (3x + 3)²

→ (3x)² + (4)² + 2×3x×4 = x² + (3x)² + (3)² + 2×3x×3

→ 9x² + 16 + 24x = x² + 9x² + 9 + 18x

→ 16 + 24x = x² + 9 + 18x

→ 16 - 9 = x² + 18x - 24x

→ 7 = x² - 6x

→ x² - 6x - 7 = 0

[ split the middle term ]

→ x² - 7x + x - 7 = 0

→ x (x - 7) + 1 (x - 7)

→ (x - 7) (x + 1)

→ x = 7 ,- 1

Therefore

x = 7 [ breadth can't be negative ]

Hence,

• breadth = x = 7cm
• length = 3x + 3 = 3(7) + 3 = 24cm