Chapter 9.4, Problem 62PFA

(a)

To determine

Find the length.

Answer to Problem 62PFA

Option B $x=12$

Explanation of Solution

Given Information: Area of Rectangle = $60c{m}^2$ , Length l = $x$ cm and Width w = $x-7$ cm

Formula Used : Area of Rectangle = $Lenght\times Width$

Calculation:

Area of Rectangle = $60c{m}^2$ , Length l = $x$ cm and Width w = $x-7$ cm.

Area of Rectangle = $Lenght\times Width$

  $60=x\left(x-7\right)$

So,

  $60=x^2-7x$

Now, simplify

  $x^2-7x-60=0$

Now, make factors of $7x$ .

  $x^2-12x+5x-60=0$

Now,

  $x\left(x-12\right)+5\left(x-12\right)=0$

Now,

  $\left(x+5\right)\left(x-12\right)=0$

Hence,

  $x=-5$ or $x=12$

Length $l=x=12$ cm

Width $w=x-7=12-7=5$ cm

(b)

To determine

Find the perimeter.

Answer to Problem 62PFA

  $34$ cm

Explanation of Solution

Given Information: Length l = $12$ cm and Width w = $5$ cm

Formula Used : Perimeter of Rectangle = $2\times \left(Lenght+Width\right)$

Calculation:

Length l = $12$ cm and Width w = $5$ cm

Perimeter of Rectangle = $2\times \left(Lenght+Width\right)$

So,

Perimeter of Rectangle = $2\times \left(12+5\right)$ cm

Now,

Perimeter of Rectangle = $2\times 17$ cm

Hence,

Perimeter of Rectangle = $34$ cm