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STALIN [3.7K]
3 years ago
5

The figure shows a right triangle. Find the length of the shortest side of the triangle.

Mathematics
2 answers:
Norma-Jean [14]3 years ago
6 0

Answer:

x= 18cm

Step-by-step explanation:

Applying pythagoras' rule

(x)²+(x+6)²=(x+12)²

Open the brackets

x²+x²+12x+36=x²+24x+144

Collect like terms to the LHS

x²+x²-x²+12x-24x+36-144=0

x²-12x-108=0

Solving the quadratic equation

a=1,b= - 24,c= - 108,ac= - 108

Factors are - 18 & +6

x²-18x+6x-108=0

(x²-18x)+(6x-108)=0

x(x-18)+6(x-18)=0

(x-18)(x+6)=0

x-18=0 or x+6=0

x=0+18 or x=0-6

x=18 or x= - 6

In cases like this it's the positive answers that are chosen

Therefore, x=18cm

Nata [24]3 years ago
3 0
I don’t see a image tho ?
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Given that, the length of the garden is 2(x+6)feet and width is 3.5x feet.

So, length : l = 2(x+6) and width = 3.5x.

To find the fence of the garden we need to find the perimeter of the rectangle.

Formula to find the perimeter is:

p = 2l + 2b

= 2*2(x+6) + 2*3.5x

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= 4x + 24 + 7x By distribution property.

= 11x + 24 Combining the like terms.

So, he need to buy 11x + 24 feet fencing.

Hope this helps you!

4 0
3 years ago
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8 0
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A student sets up the following equation to convert a measurement. Fill in the missing part of the equation
fomenos

Answer:

We have the equation:

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So we want to transform 1/mm to 1/cm.

We know that:

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1 = 10mm/1cm (we want to have mm on the numerator, so it cancelates with the mm in the denominator)

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4 0
3 years ago
The data show the traveler spend- ing in billions of dollars for a recent year for a sample of the states. Find the range, varia
Svetllana [295]

Solution :

Given data :

20.1     33.5     21.7      58.4     23.2     110.8     30.9

24.0    74.8     60.0

n = 10

Range : Arranging from lowest to highest.

20.1,   21.7,   23.2,    24.0,   30.9,    33.5,    58.4,    60.0,    74.8,   110.8

Range = low highest value - lowest value

           = 110.8 - 20.1

           = 90.7

Mean = $\frac{\sum x}{n}$

         $=\frac{20.1+21.7+23.2+24.0+30.9+33.5+58.4+60.0+74.8+110.8}{10}$

          $=\frac{457.4}{10}$

         $=45.74$

Sample standard deviation :

$S=\sqrt{\frac{1}{n-1}\sum(x-\mu)^2}$

$S=\sqrt{\frac{1}{10-1}(20.1-45.74)^2+(21.7-45.74)^2+(23.2-45.74)^2+(24.0-45.74)^2+(30.9-45)^2}$  

      \sqrt{(33.5-45.74)^2+(58.4-45.74)^2+(60.0-45.74)^2+(74.8-45.74)^2+(110.8-45.74)^2}

$S=\sqrt{\frac{1}{9}(657.4+577.9+508.0+472.6+220.2+149.8+160.2+203.3+844.4+4232.8)}$$S=\sqrt{\frac{1}{9}(8026.96)}$

$S=\sqrt{891.88}$

S = 29.8644

Variance = S^2

               =(29.8644)^2

               = 891.8823

6 0
2 years ago
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