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3 years ago

The perimeter of the triangle is 44cm.if it’s sides are in the ratio 9:7:6.find its area

Mathematics

1 answer:

shepuryov [24]3 years ago

3 0

Answer:

The area is 83.905 cm^3

Step-by-step explanation:

The total ratio is 9 + 7 + 6 = 22

So the length of the sides are as follows;

9/22 * 44 = 18 cm

7/22 * 44 = 14 cm

6/22 * 44 = 12cm

we can use Heron’s formula to find the area of the triangle

we find a first

s = (a + b + c)/2 = (18+14+12)/2 = 44/2 = 22

Mathematically, the Heron’s formula is as follows;

A = √s(s-a)(s-b)(s-c)

where a, b and c are 18,14 and 12 respectively

Plugging the values, we have;

A = √22(22-18)(22-14)(22-12)

A = √(22 * 4 * 8 * 10)

A = √(7,040)

A = 83.905 cm^3

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Prove that the product of any two consecutive natural numbers is even.

Vitek1552 [10]

Answer with Step-by-step explanation:

Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'

Thus the product of the 2 numbers is given by

$Product=n(n+1)\\\\$

We know that the sum of 'n' consecutive natural numbers starting from 1 is

$S_n=\frac{n(n+1)}{2}\\\\\therefore n(n+1)=2\times S_n............(i)$

Thus from equation 'i' we can write

$Product=2\times S_n$

As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.

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3 years ago

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3 years ago

Read 2 more answers

A uniform border on a framed photograph has the same area as the photograph. What are the outside dimensions of the border if th

Black_prince [1.1K]

Given dimension of photograph = 25cm * 20cm

So area of photograph = 500cm²

Now, let the width of frame border be = x

So, dimensions of photograph + frame= (25 + 2x)*(20 + 2x)

As given, the area of frame is same as photograph , so

Area of picture + frame = 1000cm ²

Hence, area equals

$4x^{2}+90x+500=1000$

$4x^{2}+90x-500=0$

$2x^{2}+45x-250=0$

Solving this quadratic equation,

For the quadratic equation of the form $ax^{2}+bx+c=0$ , solution is:

x1,2 = $\frac{-b+\sqrt{b^{2}-4ac}}{2a}$

Now putting a=2, b=45, c= -250 and solving he above equation, we get two values of x.

x = -27.11 (discard it as it is negative) and

x = 4.61 cm

Hence the dimensions of the frame are:

20+2x = 20+2(4.61) = 29.22 cm

25+2x = 25+2(4.61) = 34.22 cm

7 0

3 years ago

Find the slope of the line that passes through (4,1) and (7,5)

Alborosie

Answer:

4/3

Step-by-step explanation:

5 0

3 years ago

Find m<1 and m<3 in the kite. the diagram is not drawn to scale.

nikklg [1K]

Answer: Choice c. 39; 51

======================================================

Explanation:

Using the SSS congruence theorem, we can show that triangle ABC is congruent to triangle ADC. This in turn means that angle BAC is congruent to angle DAC as these are corresponding angles.

So angle 1 is 39 degrees.

----------------------------------------

For any kite, the diagonals always are perpendicular (this can be proven using a similar idea as shown above, but a bit more steps are needed). This means they meet at a right angle, and angle 2 is 90 degrees.

Let point E be the intersection point of the diagonals.

Since angle AEB is 90, this makes angle AED also 90.

Focus entirely on triangle AED. This is a right triangle.

In this triangle, A = 39, E = 90, and D is unknown

Let's find angle D

A+E+D = 180

39+90+D = 180

129+D = 180

D = 180 - 129

D = 51

Angle D is 51 degrees, which also means angle ADB = 51 degrees. This is the measure of angle 3.

----------------------------------------

We found that

angle 1 = 39 degrees
angle 3 = 51 degrees

Therefore, the final answer is choice C

7 0

3 years ago