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kaheart [24]
3 years ago
10

The area of a triangular block is 64 square inches. If the base of the triangle is twice the height, how long are the base and h

eight of the triangle?
Mathematics
2 answers:
forsale [732]3 years ago
5 0
X=long of the base
y=long of ht height.

Area (triangle)=(b*h)/2

we suggest this system equations:
xy/2=64
x=2y
we solve this system by substitution method:
(2y)y/2=64
y²=64
y=⁺₋√64
Then, we have two solutions:
y₁=-8; invalid solution
y₂=8;    ⇒x=2y=2*8=16:

solution: 
base=16 in
height=8 in
kkurt [141]3 years ago
4 0

Answer:

Area of the triangle(A) is given by:

A = \frac{1}{2}bh             ....[1]

where,

b is the base and h is the height of the triangle.

As per the statement:

The area of a triangular block is 64 square inches.

⇒A= 64 in^2

It is given that:  If the base of the triangle is twice the height

⇒b = 2h          .....[2]

Substitute these in [1] we have;

64 = \frac{1}{2} \cdot (2h) \cdot h

⇒64 = h^2

or

h^2 = 64

⇒h = \sqrt{64} = 8 inches.

Substitute h =8 in [2] we have;

b = 2(8) = 16 in.

therefore, the base and height of the triangle are:  16 inches and 8 inches.

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I answered it but I just need someone to answer just to make sure mine are right
Artemon [7]
<h2>The missing measures of the angles are:</h2>

m\angle 1= 60^{\circ}\\\\m\angle 2= 39^{\circ}\\\\m\angle 3= 21^{\circ}\\\\m\angle 4 = 39^{\circ}\\\\m\angle 5 = 21^{\circ}

<u>Given</u>:

m\angle Z = 138^{\circ}

<em><u>Note the following:</u></em>

  • An equilateral triangle has all its three angles equal to each other. Each angle = 60^{\circ}.
  • This implies that, since \triangle WXY is equilateral, therefore, m\angle Y = m\angle XWY = m\angle XYW = 60^{\circ}

  • Base angles of an isosceles triangle are congruent to each other.
  • This implies that, since \triangle WZY is isosceles, therefore, m\angle 3 = \angle 5

Applying the above stated, let's find the measure of each angle:

  • Find m\angle 1

m\angle 1 = 60^{\circ} (an angle in an equilateral triangle equals 60 degrees)

  • Find m\angle 2

m\angle 2 = 60 - m \angle 3

m\angle 2 = 60 -\frac{1}{2}(180 - 138) (Note: \frac{1}{2}(180 - 138) = 1 $ base $ angle $ of $ \triangle WZY)

m\angle 2 = 60 -21\\\\m\angle 2 = 39^{\circ}

  • Find m\angle 3 and m\angle 5 (base angles of isosceles triangle WZY)

m\angle 3 =  \frac{1}{2}(180 - 138) (1 $ base $ angle $ of $ \triangle WZY)

m\angle 3 =  \frac{1}{2}(42) \\\\m\angle3 = 21^{\circ}

m\angle3 = m\angle 5 (base angles of isosceles triangle are congruent)

Therefore,

m\angle5 = 21^{\circ}

  • Find m\angle 4

m\angle 4 = 60 - m\angle 5

Substitute

m\angle 4 = 60 - 21\\\\m\angle 4 = 39^{\circ}

The missing measures of the angles are:

m\angle 1= 60^{\circ}\\\\ m\angle 2= 39^{\circ}\\\\m\angle 3= 21^{\circ}\\\\m\angle 4 = 39^{\circ}\\\\m\angle 5 = 21^{\circ}

Learn more here:

brainly.com/question/2944195

5 0
3 years ago
What is the value of k used to find the coordinates of a point that partitions a segment into a ratio of 5:3. Please Explain.
Dafna11 [192]

Answer:

The value of k is 5/8

Step-by-step explanation:

The value of k is found by dividing the numerator of the original ratio, 5, by the sum of the numerator and denominator of the ratio

When finding a point, P, to partition a line segment AB into the ratio a/b, we find a ratio c = a / (a + b)

According to this formula we find the value of k.

k = a/(a+b)

where a = 5

b = 3

Now plug the values in the formula:

k = 5/(5+3)

k = 5/8 ....

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10 ! (To find the median add the two middle numbers 7,13 = 20 divide 20 by two and you get 10 as your median. Mode means the most common number which means the mode is also 10)
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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