Question

The area of a rectangle is 84 cm2 .if the length is 5 cm longer than the width ,find the length of the rectangle.

Answer 1

Answer:

Length = 12 $cm$

Step-by-step explanation:

Let the width of the rectangle be $x$ $cm$.

Now, the length is 5 cm longer than the width,

∴ Length of the rectangle = width + 5 $cm$

∴ Length of the rectangle = $x$ + 5 $cm$

Now, the area of the rectangle has been given 84 $cm^{2}$.

We know the formula to calculate the area of a rectangle,

Area of a rectangle = (length) * (width)

∴ 84 = ($x$ +  5) * ($x$)

∴ 84 = $x^{2}$ + 5$x$

∴ $x^{2}$ + 5$x$ - 84 = 0

We have obtained a quadratic equation.

We can find its roots by splitting the middle term into two different terms whose subtraction equals the middle term and whose multiplication is equal to the multiplication of the coefficients of the first and last term.

∴ $x^{2}$ + 12$x$ - 7$x$ - 84 = 0

∴ $x$ * ($x$ + 12) - 7 * ($x$ + 12) = 0

∴ ($x$ - 7) * ($x$ + 12) = 0

∴ $x$ - 7 = 0  OR $x$ + 12 = 0

∴ $x$ = 7 $cm$  OR  $x$ = -12 $cm$

But, distance can never have a negative value.

∴ $x$ ≠ -12 $cm$

∴ $x$ = 7 $cm$

∴ The width of the rectangle is 7 $cm$.

We know that the length is 5 cm longer than the width.

∴ Length = 5 + 7 $cm$

∴ Length = 12 $cm$

Thank you :) <3

Answer 2

Answer:

12cm

Step-by-step explanation: