Question

Find the dimensions of a rectangle whose area is given by the expression
2x² - 7x - 15.​

Answer 1

Answer:

$(2x + 3)(x - 5)$

Step-by-step explanation:

the dimensions are given by l x b

therefore,

$2 {x}^{2} - 7x - 15 \\ = 2 {x}^{2} - 10x + 3x - 15 \\ = (2x + 3)(x - 5)$

the above factors are the dimensions.

Answer 2

Answer

• Length of rectangle = ( 2x + 3 )

• Breadth of rectangle = ( x - 5 )

Given

• Area of rectangle = 2x² - 7x - 15.

To Find

• The dimensions [ length and breadth ] of the rectangle.

Step By Step Explanation

We know that the area of the rectangle = 2x² - 7x - 15.

We need to find the dimensions [ length and breadth ] of the rectangle.

So let's do it !!

By splitting the middle term

$:\longmapsto\sf2 {x}^{2} - 7x - 15 \\ \\ :\longmapsto\sf2 {x}^{2} - 10x + 3x - 15 \\ \\:\longmapsto\sf 2x(x - 5) + 3(x - 5) \\ \\:\longmapsto\sf\red{(2x + 3)(x - 5)}$

Therefore length of rectangle = ( 2x + 3 ) and breadth of rectangle = ( x - 5 ).

__________________________