Question

the area of a rectangle is 6 X square + x-15 square units and one of its size is 3 x + 5 units find it's area and perimeter​

Answer 1

Given ,

Area of the rectangle = 6x² + x - 15

Length of one side = 3x + 5

To Find :-

Perimeter of the rectangle.

Formula :-

Area of a rectangle = L × B

where, L is the length and B is the breadth of the given rectangle.

On inserting the values in the formula

We get ,

6x² + x - 15 = (3x + 5) × B

Also, 6x² + x - 15 = (3x + 5) × (2x - 3)

=> (3x + 5) × (2x - 3) = (3x + 5) × B

=>$B = {\dfrac{(3x + 5) \times (2x - 3)}{(3x + 5)}}$

(3x + 5) & (3x + 5) gets cancelled.

Therefore, B = 2x - 3

Now ,

Perimeter of a rectangle = 2(L + B)

On inserting the values in the formula

We get ,

= 2 × (3x + 5) + (2x - 3)

= 2 × (5x + 2)

= 10x + 4

Therefore, Perimeter of the rectangle = 10x + 4.

Verification :-

Perimeter of a rectangle = 2(L + B)

=> 10x + 4 = 2{(3x + 5) + (2x - 3)}

=> 10x + 4 = 2 × (5x + 2)

=> 10x + 4 = 10x + 4

Since, LHS = RHS Hence Verified.