Question

Give possible expressions for the length and breadth of the rectangle whose area is 25²a + 35a +12.

Answer 1

Question

Give possible expressions for the length and breadth of the rectangle whose area is 25²a + 35a +12.

step by step explanation

We know that

Area of rectangle= Length× Breadth

We have,

Area= 25a²-35a+12

Area= 25a²-20a -15a + 12

Area= (25a² – 20a) – (15a – 12)

Area =5a( 5a-4)-3(5a – 4)

Area=(5a–4)(5a – 3)

Hence, the possible expressions for the length and breadth are:

Length Breadth

(i) 5a - 4 5a-3

(ii) 5a - 3 5a-4

For more information

Perimeter of Rectangle = 2(l+b)

Area of Rectangle= length× breadth

Area of Rohmbus= (d1×d2)/2

Area of Trapezium= 1/2(a+b)×h

Answer 2

Answer:

Let us first factorize the given expression 25a

2−35a+12 as shown below:

25a2−35a+12

=25a2−15a−20a+12

=5a(5a−3)−4(5a−3)

=(5a−4)(5a−3)

Therefore, the area of the rectangle is (5a−4)(5a−3) and we also know that the area of the rectangle is A=length×breadth.

(ii) Let us first factorize the given expression 24x

2

−15x as shown below:

24x

2

−15x

=x(24x−15)

Therefore, the area of the rectangle is x(24x−15) and we also know that the area of the rectangle is A=length×breadth.

Hence, the length and breadth can both be x or (24x−15).