Question

the rectangle of length 16CM more than its breadth is same in area as the square of the side 15 CM find the sides of rectangle​

Answer 1

$area \: of \: square = {side}^{2}$

$area \: of \: square \: = {15}^{2}$

225 cm^2

Now.,

let the breadth be x and breadth will be 16+x

A. T. Q.

area of rectangle =L*B

=> 225cm^2=x*(x+16)

$=> \: \: \: \: \: \: \: 225 {cm}^{2} = {x}^{2 } + 16x \\ = > \: \: \: \: \: \: \: \: \ 225{cm}^{2} \div 16 = {x}^{2 } + x \\ = > \sqrt{ \frac{225}{16} } = x$

$= > \frac{15}{4} = x \\ = > x = \frac{15}{4}$

HENCE,THE LENGTH OF RECTANGLE=X=15/4

AND, BREADTH=16+15/4=(64+15)/4=79/4. your answer

Answer 2

Answer:

Length = 25 cm and breadth = 9 cm

Step-by-step explanation:

Given :

Side of square is 15 cm.

So area of square = side × side

Area of square = 15 × 15 = 225  $cm^2$

Now Let breadth of rectangle is x cm

So length become ( x + 16 ) cm

Also given area of reatangle = area of square

According to question

( x )( x + 16 ) = 225

$\large x^2+16x-225=0\\\\\\\normal \text{By splitting mid term method we get}\\\\\\\normal x^2-9x+25x-225=0\\\\\\\normal x(x+25)x-9(x+25)=0\\\\\\\normal (x+25)(x-9)=0\\\\\\\normal \text{so we get two value x= -25 or x= 9 }\\\\\\\normal \text{Hence side cannot be negative , we get x=9}$

So length of rectangle is 9 + 16 = 25 cm and breadth = 9 cm.