Ask question

Ask question

All categories

2 years ago

5

A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10m greater than the other side.

Find the length of the fence needed to surround this garden if the area of the vegetable garden is 2184m2.

1 answer:

DanielleElmas [232]2 years ago

5 0

Answer:

The length of the fence needed to surround this garden is 188 meters.

Step-by-step explanation:

Given : A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10 m greater than the other side.

To find : The length of the fence needed to surround this garden if the area of the vegetable garden is 2184 m² ?

Solution :

Let the one side of rectangle be 'x'.

Then the other side is 'x+10'.

The area of the rectangle is 2184 m²,

i.e. $x(x+10)=2184$

$x^2+10x-2184=0$

Solve by middle term split,

$x^2+52x-42x-2184=0$

$x(x+52)-42(x+52)=0$

$(x+52)(x-42)=0$

$x=-52,42$

Reject negative value,

The side of the rectangle is 42 m.

The other side is 42+10=52 m

The perimeter of the rectangle is $P=2(l+b)$

$P=2(42+52)$

$P=2(94)$

$P=188$

Therefore, the length of the fence needed to surround this garden is 188 meter.

You might be interested in

The positive difference between the two roots of the quadratic equation $3x^2 - 7x - 8 = 0$ can be written as $\frac{\sqrt{m}}{n

Sergio [31]

3x² - 7x - 8 = 0

We're asked about square roots so we won't try to factor; we'll go right for the quadratic formula,

x = ( 7 ± √(7² - 4(3)(-8)) )/(2(3)) = (7 ± √(49+96))/6 = 7/6 ± √145/6

145 = 5×29, so no square factors. The positive difference is

d = (7/6 + √145/6) - (7/6 - √145/6) = 2√145/6 = √145/3

so m=145, n=3 for a sum of

Answer: 148

3 0

2 years ago

Read 2 more answers

A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new subs

Nitella [24]

Answer How many liters of a 20% acid solution should be mixed with 30 liters of 50% acid solution in order to obtain a 40% solution. ... x=15 liters 15*(.20 pure acid)=3 liters 30*(.50 pure acid)=15 liters That is 18 liters pure acid That is 45 liters solution *0.45 pure acid=18 liters.

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

goblinko [34]

Answer:

coordinate of point A is (a,b)

coordinate of point C is (2c,d)

slope of AD and BC = $\frac{b}{a-c}$

Step-by-step explanation:

According to midpoint formula

If we have points P $(x_{1} ,y_{1} )$ and Q $(x_{2} ,y_{2} )$

then the coordinate (x,y) of mid point of line PQ is given by

$x=\frac{x_{1} +x_{2} }{2}$ and $y=\frac{y_{1} +y_{2} }{2}$

now from the given diagram A is the mid point of line joining R(0,0) and S(2a,2b)

Using midpoint formula, coordinates of point A is given by

$x=\frac{0+2a}{2}= a$ and $y=\frac{0+2b}{2} =b$

so we have

coordinate of point A is (a,b)

Also C is the midpoint of line joining T (2c,2d) and V(2c,0)

coordinate of point C is given by

$x= \frac{2c+2c}{2} =2c$ and $y=\frac{2d+0}{2} =d$

so we have

coordinate of point C is (2c,d)

it is given that coordinate of point B is (a+c, b+d) and coordinate of D is (c,0)

If we have points P $(x_{1} ,y_{1} )$ and Q $(x_{2} ,y_{2} )$

then the slope of PQ = $\frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

hence slope of AD= $\frac{0-b }{c-a}$

= $\frac{-b}{c-a}$

= $\frac{-b}{-(a-c)}$

= $\frac{b}{a-c}$

and slope of BC = $\frac{d-(b+d)}{2c-(a+c)}$

= $\frac{d-b-d}{2c-a-c}$

= $\frac{-b}{c-a}$

= $\frac{b}{a-c}$

so we have

slope of AD and BC = $\frac{b}{a-c}$

7 0

2 years ago

Read 2 more answers

Alexa owns a total of 45 fiction and nonfiction books. If the number of fiction books is 15 more than 4 times the number of nonf

Vikentia [17]

What are the choices?

4 0

2 years ago

Paulo uses an instrument called a densitometer to check that he has the correct ink colour. For this print job the acceptable ra

sattari [20]

<span>If the range of the answer should be +/- 10% of the particular value, then you have to solve for the percentage of that particular value. Since the value given is 1.8, we thus want to find 10% of that: 1.8 * 10/100 = 0.18 Then, add this value to the original value of 1.8: 1.8+0.18 = 1.98 Next, subtract .18 from from the original value of 1.8: 1.8-0.18 = 1.62 The range will be between these two numbers, so the range is from 1.62 to 1.98.</span>

5 0

2 years ago