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max2010maxim [7]
3 years ago
11

the figure below,not drawn to scale ,is made up of two identical right angled triangles overlapping each other. find the area of

the shaded part ABCD, where AD equals to 3cm.

Mathematics
1 answer:
Shtirlitz [24]3 years ago
8 0
We develop two equations based on the given diagram. We let x be the length from C to the point meeting the endpoint of 5. We let y be the length of CD. 

First, we determine the length from D to the endpoint of line measuring 9 cm. We use the Pythagorean theorem.
      l = sqrt ((3)² + 5²) 
      l = 5.83

Then, the equations that can be developed or established are:
    x² + 6² = y²
   9² + (5 + x)² = (y + 5.83)²

In solving for x and y, we use substitution.
From the first equation,
  y = sqrt (x² + 36)
We substitute this to the second equation y. 

The value of x is 9.51. 

y = sqrt (9.51² + 36) = 11.25.

Calculate for the area of the bigger triangle.
  A = 0.5(9 cm)(5 + 9.51 cm) = 65.295 cm²

Also calculate for the area of the smaller triangle,
  A = (0.5)(6 cm)(9.51 cm)  = 28.53 cm²

The difference between the areas is 36.765 cm².

<em>ANSWER: 36.77 cm²</em>
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7 0
3 years ago
Can the sum of two mixed numbers be equal to 2.Explain why or why not
Verdich [7]

Answer:

yes

Step-by-step explanation:

yes. because 1 and 1/2 added to 1/2 equals 2.

but...

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6 0
3 years ago
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nydimaria [60]

The area of a circle is

A=\pi r^2

The radius is half the diameter, so we have

A=\pi \left(\dfrac{11}{2}\right)^2

5 0
3 years ago
What's the distance between (-2, 5) and (8, 5)
Wewaii [24]

Answer:

10

Explanation:

The distance between two points of coordinates (x1, y1) and (x2, y2) can be calculated as:

\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}

So, the distance between (-2, 5) and (8, 5) is equal to:

\begin{gathered} \sqrt[]{(8-(-2))^2+(5-5)^2} \\ \sqrt[]{(8+2)^2+(0_{})^2} \\ \sqrt[]{(10)^2+0} \\ \sqrt[]{100} \\ 10 \end{gathered}

Then, the distance between (-2, 5) and (8, 5) is 10.

7 0
1 year ago
Please help fast<br> The graph shows the function f(x)
DedPeter [7]

Answer:

3/1

Step-by-step explanation:

The average rate of change is the distance between y values divided by the distance between x values. We know this as rise/run or slope for linear equations. For non-linear equations, we calculate the average over an interval.

This function has y-values of -1 at x=0 and 5 at x=2.

We add -1+5=6 and divide this by 2-0=2.

6/2=3.

The y-values on average change 3 units for every 1 unit of the x-values.

4 0
3 years ago
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