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3 years ago

I need these answersss

Mathematics

2 answers:

Katen [24]3 years ago

8 0

Hello!

There are two ways to solve this.

First we can find the answer of the whole square, including the gap in the middle. This gives us 120. Now, if we subtract the area of the white rectangle (the part that doesn't exist), we get 106 m.

Just to verify, we can split the polygon into three polygons by splitting it with two lines, each bordering the edges of the white rectangle this gives us 48+48+10
This gives us 106, which matches our original answer.

This means that the area of the figure is 106 m².

I hope this helps!

pav-90 [236]3 years ago

4 0

Hi there!

Let's break this figure up into three rectangles. Two are congruent and one is smaller.

The area of the larger rectangles:
2(4 x 12) = 96

Area of the smaller rectangle:
2 x 5 = 10

Lastly, we'll add the areas together:
96 + 10 = 106

Area: 106 meters^2

Hope this helps!! :)

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A certain triangle has a perimeter of 3084 mi. The shortest side measures 76 mi less than the middle side, and the longest side

kari74 [83]

shortest side: 851

middle side:927

longest side : 1306

Explanation

Step 1

Let

x represents the shortest side

y represents the middle side

z represents the longest side

so, set the equations

a) the perimeter of a rectangle is the sum of the sides, so

$\begin{gathered} \text{Perimeter= side1+side2+side3} \\ replace \\ 3084=x+y+z \\ x+y+z=3084\Rightarrow\text{ Equation(1)} \end{gathered}$

b) The shortest side measures 76 mi less than the middle side( in other words, you have to subtract 76 from middle side to get the shortest side)

$x=y-76\Rightarrow equation(2)$

c) and the longest side measures 379 mi more than the middle side,( in other words, you have to add 379 to middle side to obtain the longest side)

$z=y+379\Rightarrow equation(3)$

Step 2

solve the equations

a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)

$\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\ \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}$

now, replace the y value in equatino (2) to find x

$\begin{gathered} x=y-76\Rightarrow equation(2) \\ x=927-76 \\ x=851 \end{gathered}$

c) finally, prelace x and y value in equation (1) to find z

$\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}$

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middle side:927

longest side : 1306

I hope this helps you

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