Question

prayer hall consists of a carpet area of a carpet area of 300 sq.m with its length (2x + 1) m
and breadth x m

The length of the prayer hall is
a) 24 m
b) 22 m
c) 25 m
d) 20 m

The breadth of the prayer hall is
а) 12 m
b) 24 m
c) 48 m
d) 22 m

The perimeter of the prayer hall is
a) 72 m
b) 74 m
c) 37 m
d) 62 m

In the above figure the value of AB is
a) greater
than the value of AD
b) smaller
c) equal
d) not equal

The value of BD in the prayer hall
а) 27.73 m
b) 27.90 m
c) 25 m
d) 29 m​

Answer 1

Given : prayer hall consists of a carpet area of a carpet area of 300 sq.m with its length (2x + 1) m   and breadth x m

To Find : The length of the prayer hall is  

a) 24 m   b) 22 m  c) 25 m   d) 20 m

The breadth of the prayer hall is

а) 12 m   b) 24 m   c) 48 m   d) 22 m

The perimeter of the prayer hall is  

a) 72 m   b) 74 m   c) 37 m   d) 62 m

In the above figure the value of AB is

a) greater  than the value of AD   b) smaller   c) equal   d) not equal

The value of BD in the prayer hall  

а) 27.73 m  b) 27.90 m   c) 25 m   d) 29 m

Solution:

Length of Carpet Area = 2x + 1 m

Breadth of Carpet Area = x m

Area of Carpet  == (2x + 1)x  m²

= 2x²  + x  m²

2x²  + x = 300

=>  2x²  + x - 300 = 0

=> 2x²  -24x + 25x - 300 = 0

=> 2x(x - 12) + 25(x - 12) = 0

=> (2x + 25)(x - 12) = 0

=> x = - 25/2  or  12

x can not be -ve as its  breadth

Hence x = 12

Breadth = 12 m

Length = 2x + 1 = 2(12) + 1 = 25 m

The length of the prayer hall is   25 m

The breadth of the prayer hall is  12 m

perimeter of the prayer hall  = 2(25 + 12)  = 74 m

AB = 25 m  , AD = 12 m

value of AB is  greater than value of AD

Value of BD  =√25² + 12²  = 27.73 m

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