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4 years ago

12

What is the value of x?

1 answer:

alina1380 [7]4 years ago

7 0

Answer:

<h2>x = 4</h2>

Step-by-step explanation:

Look at the picture.

We have the triangles 30° - 60° - 90° and 45° - 45° - 90°.

The sides are in proportions:

30° - 60° - 90° ⇒ 1 : √3 : 2

45° - 45° - 90° ⇒ 1 : 1 : √2

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

$SR=ST\sqrt3\to ST\sqrt3=2\sqrt3\qquad\text{divide both sides by}\ \sqrt3\\\\ST=2\\\\TR=2ST\to TR=2(2)=4\\\\RQ=TR\to RQ=4\to x=4$

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The upper-left coordinates on a rectangle are (-4,4), and the upper-right coordinates are (4,4).The rectangle has an area of 8 s

maw [93]

Answer:

Then the coordinate of point $C$ is $(4,3)$ , and the coordinate of point $D$ is $(-4,3)$ .

Step-by-step explanation:

Given that,

The upper-left coordinate on a rectangle is $(-4,4)$ .

The upper-right coordinate on a rectangle is $(4,4)$ .

Area of rectangle is $8$ square unit.

Let, $ABCD$ is a rectangle.

The coordinate of point $A$ is $(-4,4)$ and the coordinate of point $B$ is $(4,4)$ .

Diagram of rectangle $ABCD$ is shown below:

Now,

$AB=$ $\sqrt{(4+4)^{2}+(4-4)^{2} }$

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$=\sqrt{64}$

$= 8\ unit$

∵Area of rectangle = Length $\times$ Breadth

$8$ square unit = $8\ unit$ $\times Breadth$

∴ Breadth $=1\ unit$

$BC=\sqrt{(4-4)^{2}+(y-4)^{2} }$

$=\sqrt{(y-4)^{2} }$

⇒ $1$ $=\sqrt{(y-4)^{2} }$

squaring both sides, we get

⇒ $1=(y-4)^{2}$

⇒ $(y-4)$ = ± $1$

∴ $y=3$

Then the coordinate of point $C$ is $(4,3)$ , and the coordinate of point $D$ is $(-4,3)$ .

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