Question

The length of a rectangle is 5 inches more than its width,x.The area of a rectangle can be represented by the equation x^2=+5X=300.What are the meausres of the width and the length?

Answer 1

Answer:

$Width=15\ inLength=20\ in$

Step-by-step explanation:

x^2=+5X=300

Let

x = the width of the rectangle

y =  the length of the rectangle

we know that

the area of the rectangle is equal to

A=xy ___ equation 1

y=x+5 ___equation 2

substitute equation 2 in equation 1

$A=x(x+5)A=x^{2}+5x$

$x^{2} +5x=300$ ------> given problem

so

the area of the rectangle is equal to

$A=300\ in^{2}$

Solve the quadratic equation

$x^{2} +5x-300=0$

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

we have

$x^{2} +5x-300=0$

so

$a=1\\b=5\\c=-300$

substitute in the formula

$x=\frac{-5 \pm\sqrt{5^{2}-4(1)(-300)}} {2(1)}$

$x=\frac{-5 \pm \sqrt{1225}} {2}$

$x=\frac{-5 \pm 35} {2}$

$x=\frac{-5+35} {2}=15$

$x=\frac{-5-35} {2}=-20$

The solution is

$x=15\ in$

Find the value of y

y=x+5

$y=15+5=20\ in$

$Width=15\ inLength=20\ in$

Answer 2

Answer:

Width = 15 inches

length = 20 inches

Step-by-step explanation:

Let

width  = x

According to the question the length of the rectangle is 5 inches more than it width. Therefore,

length = x + 5

Area of a rectangle = LW

where

L = length

W = width

Area of the rectangle

x² + 5x = 300

x² + 5x - 300 = 0

Find the number you can multiply to give you -300 and add to give you 5. The numbers are -15 and 20

x² - 15x + 20x -300 = 0

x(x - 15) + 20(x - 15)

(x - 15)(x + 20) = 0

x = 15 or - 20

we can't use - 20 since it is negative.

Recall

width = x = 15

length = x + 5 = 15 + 5 = 20

Width = 15 inches

length = 20 inches