Question

Rectangles are drawn on line segments of fixed lengths. When the breadths are 6 m
and 5 m respectively the sum of the areas of the rectangles is 83 m2. But if the breadths
are 5 m and 4 m respectively the sum of the areas is 68 m2. Find the sum of the areas
of the squares drawn on the line segments.

Also follow me.
​

Answer 1

Answer:

The sum of the areas of the square drawn on the line segments is 113 .

Step-by-step explanation:

Given:

Let length of first rectangle  =  x m  

Length of Second rectangle  =  y m  

We know Area of rectangle  =  

So,

Area of first rectangle = 6x

Area of second rectangle = 5y  

According to first condition, we get  

6x  + 5y  = 83                                                [ 1 ]

Now breadth of first rectangle  =  5 m and breadth of second rectangle = 4 m  

So, according to second condition we get  

5x + 4y = 68                                                [ 2 ]

Now we multiply equation (1) by 4 , we get  

24x + 20y = 332                                         [3]

And Mutiply equation (2) by 5, we get

25x + 20y = 340                                           [4]

Now we subtract equation(3) from equation (4), we get  

25x + 20y - (24x + 20y) = 340 - 332

25x + 20y - 24x - 20y = 8

x = 8    

Substitute this value in equation (2), we get  

5 ( 8 ) + 4y = 68  

40 + 4y = 68

4y = 68 - 40

4y = 28  

y = 7  

So,  length of first rectangle = 8m  and we draw a square on this base so, Area of this square =    

And  length of Second rectangle = 7m and we draw a square on this base so,

Area of this square =    

Then sum of area of these two square = 64 + 49 = 113  

Hence the sum of the areas of the square drawn on the line segments is 113 .