A rectangular garden is 27 meters long and 21 meter side. Find the

The length of a rectangle is 5 inches more than its vedth. The area of the rectangle is equal to

jarptica [38.1K]

Answer:

The width = x = 14

The length = x+5 = 14+5 = 19

Step-by-step explanation:

Let l = length, w = width, A = area = l×w , and P = perimeter = 2(l+w)

Let 'x' be the width

As the length 'l' of a rectangle is 5 inches more than its width.

so the length will be = x+5

As the Area of the rectangle is equal to 2 inches more than 4 times the perimeter.

A = 4P + 2

so the equation becomes

l × w = 4×2(l+w)+2

substituting w=x, l = x+5,

(x+5)x = 8(x+5+x)+2

x²+5x = 8(5+2x)+2

x²+5x = 40+16x+2

x²+5x = 16x+42

x²+5x-16x-42 =0

x²-11x-42=0

$x^2-11x=42$

$\mathrm{Add\:}a^2=\left(-\frac{11}{2}\right)^2\mathrm{\:to\:both\:sides}$

$x^2-11x+\left(-\frac{11}{2}\right)^2=42+\left(-\frac{11}{2}\right)^2$

$x^2-11x+\left(-\frac{11}{2}\right)^2=\frac{289}{4}$

$\left(x-\frac{11}{2}\right)^2=\frac{289}{4}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solving

$x-\frac{11}{2}=\sqrt{\frac{289}{4}}$

$x-\frac{11}{2}=\frac{\sqrt{289}}{\sqrt{4}}$

$x-\frac{11}{2}=\frac{\sqrt{289}}{2}$

$x-\frac{11}{2}=\frac{17}{2}$

$x-\frac{11}{2}+\frac{11}{2}=\frac{17}{2}+\frac{11}{2}$

$x=14$

similarly solving

$x-\frac{11}{2}=-\sqrt{\frac{289}{4}}$

$x-\frac{11}{2}=-\frac{17}{2}$

$x-\frac{11}{2}+\frac{11}{2}=-\frac{17}{2}+\frac{11}{2}$

$x=-3$

so

x = 14, or x = -3

As the width 'x' can not be negative.

so x = 14

Thus,

The width = x = 14

The length = x+5 = 14+5 = 19

6 0

3 years ago

Choose the equation that correctly uses the Pythagorean Theorem for the given right<br> triangle.

Zina [86]

3.8^2 + 6.8^2 = x^2 because the Pythagorean theorem is a^2 + b^2 = c^2 which c is the longest side or c in this case

5 0

2 years ago

hyun is comparing two numbers. he knows the larger number is twice the value of 4 more than the smaller number, x. he also knows

irinina [24]

Let b>a...

b=2(a+4)

b=2a+8 then we are told that:

b-a=11 using b found above in this equation gives you:

2a+8-a=11 combining like terms on left side

a+8=11 subtracting 8 from both sides

a=3

So the smaller number is 3.

...

since b=2a+8

b=14

check..

b=2(a+4)

14=2(3+4)

14=2(7)

14=14

and

b-a=11

14-3=11

11=11

6 0

4 years ago

Read 2 more answers

Six more than 1/5 a number is 12. What is the number

suter [353]

Answer:

Step-by-step explanation:

let x be the number

6+1/5x=12

1/5x=12-6

1/5x=6

x=5*6

x=30

check: 6+(1/5*30)=6+6=12

8 0

3 years ago

You get brainliest if answered correctly −6.5(n−5)=18.2

scZoUnD [109]

The value of n would be 2.2 if that's what you wanted.

3 0

3 years ago