Question

PLEASE..SOLVE THIS...

✒The perimeter of a rectangle and squate are equal,but the area of the former is 225 sq.m less than the later.Find the length and breadth of the rectangle.

Answer 1

Answer:

$\colorbox{\red a \geqslant 15}$

$\huge\underline\textsf{Explantion:- }$

Let,L = length of the rectangle

B = breadth

A = side of Square

Now, given that

perimeter of rectangle =perimeter of square

$\large\underline\textsf{ Formula Used }$

=2(l+b)=4a

=l+b=2a

Now, we have given the

Area of rectangle =Are of square-225

LB= a^2

a^2-15^2

$\large\underline\textsf{Identity used:- }$

$\boxed{(a {}^{2} - b {}^{2} ) = (a + b)(a - b)}$

Now,

LB =(a+15)(a-15)

Now ,as length is always greater than than the breadth of a rectangle.

$\therefore$ L=a+15 and B=a-15

And ,as the length of any side is always positive so,

$\boxed{a - 15 \geqslant 0 = > a \geqslant 15}$

L=a +15

& B=a-15

$</strong><strong>\</strong><strong>boxed</strong><strong>{</strong><strong>a \geqslant 15</strong><strong>}</strong><strong>$

Answer 2

Answer:

$\implies\:$a $\geqslant$ 15

Explanation:

Let,

• L = Length of the rectangle
• B = Breadth of the rectangle
• "and" A = Side of the square

Now Given That,

Perimeter of rectangle = Perimeter of square

= 2(length + breadth) = 4a

= length + breadth = 2a

Now, We have given that,

Area of rectangle=Area of square-225

LB = a² - 225

⠀ = a² - 15²

LB = (a + 15) (a - 15)

[ ∴ a² - b² = (a + b) (a - b)]

Now, as length is always greater than the breadth of a rectangle

∴ Length = a + 15 and Breadth = a - 15

And, as the length of any side is always position, So,

a - 15 $\geqslant$ 0 => a $\geqslant$ 15

• Length = a + 15
• Breadth = a - 15

$\implies\:$ a $\geqslant$ 15.