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larisa [96]
3 years ago
14

Find the value of x for the right triangle.

Mathematics
1 answer:
Ivahew [28]3 years ago
3 0

the value of x for the right triangle is 60

Step-by-step explanation:

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50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle
aalyn [17]

Answer:

EF=4\sqrt{3}

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

A_{\text{rect}}=8(6)=48\text{ cm}^2

The area of the triangle is 1/4 of this. Therefore:

\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

\displaystyle 12=\frac{1}{2}(DE)(DF)

Since DE = DF:

24=DF^2

Thus:

DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

(DE)^2+(DF)^2=(EF)^2

Therefore:

(2\sqrt6)^2+(2\sqrt6)^2=EF^2

Square:

24+24=EF^2

Add:

EF^2=48

And finally, we can take the square root of both sides:

EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}

6 0
3 years ago
Read 2 more answers
The price of an item has risen to $152 today. Yesterday it was $95. Find the percentage increase.
Oksanka [162]

Answer:

60% increase

Step-by-step explanation:

152 - 95 = -57

57 / 95 = 0.6

0.6 x 100 = 60

5 0
2 years ago
Find the slope of the line passing through the points (-5,3) and (-5,-7)
padilas [110]

Answer:

The slope is Undefined.

Step-by-step explanation:

8 0
3 years ago
suppose A and B are complementary angles, m a =(3x+5) and m b= (2x-15). Solve for x and then find m a and m b
vlada-n [284]
2 angles are complementary if the sum of their measures is 90°.

For example  if m(P) = 41°  and m(Q)=49°, then P and Q are complementary.


Thus A and B are complementary means that m(A)=m(B)=90°:

(3x+5°) + (2x-15°) =90°

5x-10°=90°

5x=100°

x=20°



Thus 

m(A)=3x+5°=3* 20°+5°=60°+5°=65°

m(B)=2x-15°=2*20°-15°=40°-15°=25°
8 0
3 years ago
The measure of arc QS is (4x – 18)°.
Zigmanuir [339]

Answer: 49.5

Step-by-step explanation:

7 0
3 years ago
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