Question

The diagonalof rectangular plot is 34cm and its perimeter is 92cm find its area​

Answer 1

perimeter=2(a+b)

2(a+b)=92

a+b=46

diagnols a^+b^=34^2

(a+b)^2-a^2-b^2=2ab

46^2-34^2=2ab

ab=960/2

=480

Answer 2

${\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}}$

Question

⠀⠀⠀⠀⠀• The diagonalof rectangular plot is 34cm ⠀⠀⠀⠀⠀and its perimeter is 92cm find its area?

Answer

⠀⠀⠀⠀⠀• Area = 480cm²

Given

⠀⠀⠀⠀⠀• Diagonal 34cm

⠀⠀⠀⠀⠀• Perimeter = 92 cm

To Calculate

⠀⠀⠀⠀⠀• Area

Step by step explanation

Diagonal of Rectangle plot = 34 cm (Given)

Perimeter of rectangle plot = 92 cm ( Given )

We know that

${\boxed{\red{\tt{ ( Diagonal )² = ( Length)² + ( breadth)² ⇢ ( PGT) }}}}$

➺ (34)²= (l)² +(b)²

➺ l²+ b²= 1156_____________(1)

Now, We know that

${\boxed{\red{\tt{Perimeter\:of \: rectangle ⇢ 2( l+b) }}}}$

➺ P= 2(l+b)

➺ 92 = 2 ( l+b)

➺ (l+b) = 92/2

➺( l+b) = 46

↝ Square Both Side

➥ (l+b)²= 46²

➥ l²+b²+ 2×l×b= 2116

➥ l²+b²+ 2lb= 2116

↝ From eq1

↝ Putting Value of l²+b²

➺ 1156+2lb=2116

➺ 2lb = 2116-1156

➺ 2lb = 960

➺ lb= 960/2

➺ lb= 480_________(2)

Now,

We know that

${\boxed{\red{\tt{Area\: of \: Rectangle ⇢ l×b}}}}$

➺ A= l×b

From eq2

➺ A= 480

${\huge{\underline{\underline{\sf{\blue{Hence :-}}}}}}$

⠀⠀⠀⠀⠀• Area = 480cm²

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