Question

3.The area of a lot is 4a2 – 225 square meters, if the length is 2a + 15 meters what is the width of the lot? 4. in questio no.3 what will be the exact width of the lot if the value of a is 10?

Answer 1

Answer:

3. Width of the lot $=2a - 15$ $meters$

4. If the value of a is 10, the width will be $= 5 meters$

Step-by-step explanation:

3.

$4a^2 - 225$

$=(2a)^2 - (15)^2$

$=(2a + 15)(2a - 15)$  [using the identity $a^2 - b^2 = (a + b)(a - b)$]

Width of the lot $=\frac{Area}{Length}$

$=\frac{4a^2 - 225}{2a + 15}$

$=\frac{(2a + 15)(2a - 15)}{(2a + 15)}$

$=2a - 15$ meters

4. If the value of a is 10, the width will be $=(2).(10) - 15 m = 20 - 15 m = 5 m$

Answer 2

Given :-

• The area of a lot is = 4a^2 - 225 m^2

• The length of the lot = 2a + 15 m

Solution 1 :-

As we know that,

Area of rectangle = Length * Breath

Area = 4a^2 - 225m^5 , Length = 2a + 15m ,

Breath = ?

Let the breath be x

Put the required values in the formula,

4a^2 - 225 = 2a + 15 * X

( 2a)^2 - (15)^2 = 2a + 15 * x

[ Using identity a^2 - b^2 = ( a + b)( a - b) ]

(2a + 15) ( 2a - 15 ) = 2a + 15 * x

( 2a + 15) ( 2a - 15 ) / 2a + 15 = x

x = 2a - 15

Hence, The breath of a lot

= 2a - 15 m

Question 2 :-

What will be the exact value of lot if the value of a = 10 ?

Solution 2 : -

In the 3 question , we find the

Width of the lot = 2a - 15

Here, The value of a = 10

Therefore

The width of the lot = 2 * 10 - 15

The width of the lot = 20 - 15 = 5

Hence, The width of the lot = 5m $.$