Question

please give the answer really urgent​

Answer 1

QUESTION :

The length of a rectangle is 1 cm more than its breadth. The diagonal is 29 cm. Find the area of rectangle.

EXPLANATION :

Given :-

• The length of a rectangle is 1 cm more than its breadth.
• The diagonal is 29 cm.

To find :-

• Find the area of rectangle.

Solution :-

Let the breadth of the rectangle be x cm.

✪The length of a rectangle is 1 cm more than its breadth ✪

Length = (x+1) cm

We know,

$\sf{Diagonal\: of\: rectangle=\sqrt{Length^2+Breadth^2}}$

✪ Diagonal of rectangle= 29 cm✪

According to the question,

$\sf{\sqrt{(x+1)^2+x^2}=29}$

$\implies\sf{\sqrt{x^2+2x+1+x^2}=29}$

$\implies\sf{2x^2+2x+1=29^2}$

$\implies\sf{2x^2+2x+1=841}$

$\implies\sf{2x^2+2x+1-841=0}$

$\implies\sf{2x^2+2x-840=0}$

$\implies\sf{x^2+x-420=0}$

$\implies\sf{x^2+(21-20)x-420=0}$

$\implies\sf{x^2+21x-20x-420=0}$

$\implies\sf{x(x+21)-20(x+21)=0}$

$\implies\sf{(x+21)(x-20)=0}$

Either,

x+21=0

→ x = -21

Or,

x-20=0

→ x = 20

★Breadth of the rectangle= 20 cm

★Length of the rectangle= (20+1) cm = 21 cm.

We know,

$\sf{Area\: of\: rectangle=Length\times\: Breadth}$

Area =( 21 × 20 ) cm²

→ Area = 420 cm ²

Therefore, the area of the rectangle is 420 cm².

____________________

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$Area = 420cm²

$\large\underline\mathrm{Given:-}$

• The length of rectangle is 1 centimetre more than and its breadth.
• the diagonal is 29cm.

$\large\underline\mathrm{To \: find}$

• find the breadth of the rectangle be x cm.
• The length of a rectangle is 1 cm more than its breadth.

$\large\underline\mathrm{Length \: = \: (x \: + \: 1)cm}$

$\large\underline\mathrm{Diagonal \: of \: rectangle \: = \: √l² \: + \: b²}$

$\implies$ √(x + 1)² + x² = 29

$\implies$ √x² + 2x + 1 + x² = 29

$\implies$ 2x² + 2x + 1 = 29²

$\implies$ 2x² + 2x + 1 = 841

$\implies$ 2x² + 2x + 840 = 0

$\implies$ x² + x + 420 = 0

$\implies$ x² + (21 - 20) x - 420 = 0

$\implies$ x² + 21x - 20x - 420 = 0

$\implies$ x(x + 21) - 20(x + 21) = 0

$\implies$ (x + 21)(x - 20) = 0

$\implies$ x + 21= 0

$\implies$ x = -21

$\implies$ x - 20 = 0

$\implies$ x = 20

$\implies$Breadth = x = 20cm

$\implies$Length = (x + 1) = 20 + 1 = 21cm

$\large\underline\mathrm{Area \: of \: rectangle \: = \: L. \: × \: B:-}$

$\implies$Area = 21 × 20

$\implies$Area = 420cm²

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{the \: area \: of \: the \: rectangle \: is \: 420cm².}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$