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Westkost [7]
3 years ago
8

The corresponding angles in △ABC are congruent to the corresponding angles in △FGH. The measures of two corresponding sides of t

he triangles are given:
AB=4
AC=6
FG=x+11
FH=7x

What is the length of FH?
Mathematics
1 answer:
Lina20 [59]3 years ago
4 0
Since <span>The corresponding angles in △ABC are congruent to the corresponding angles in △FGH, so they are similar triangles. in a similar triangles, their corresponding sides are in proportion.
so AB / AC = FG / FH
substitute the given values
4 / 6 = x + 11 / 7x
then solve for x
28x = 6x + 66
22x = 66
x = 3

so the value of FH = 7x = 7(3) = 31</span>
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It took team rise over run 1 2/3 hours to hike 4 2/3 miles. What is their average speed in miles per hour?
pogonyaev

To find their average miles per hour we can divide the total miles by the hour used:

4 2/3 ÷ 1 2/3

=4x3+2/3 ÷ 1x3+2/3

=14/3 ÷ 5/3

In division, when we switch the place of numerator and denominator, we can change it to multiplication which makes the calculation easier as we can factorize the numbers.

=14/3 x 3/5

Factorize 3 in both amounts:

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=2.8 miles/hour

Therefore their average speed is 2.8 miles/hour.

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A helicopter blade does 3206 full turns in 7 minutes. Work out the number of full turns per minute? Then work out how many turns
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458 turns/min ----- 13740/30 min

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Francine is selling ice cream from her shack on the ocean. She opens the shack
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What is the height of the triangle? 12 units 24 units 36 units 72 units.
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Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side. The height of the tringle is 24 units. Hence option 2 is the correct option.

<h3>Given information-</h3>

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is 16 \sqrt{3} units.

As all the sides are equal thus the \Delta MNO is a equilateral triangle in which the height of the divides the triangle into two equal part of the length 8\sqrt{3} at point <em>R.</em>

<h3>Height of the triangle-</h3>

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the  \Delta MRN, the length of the hypotenuse is 16 \sqrt{3} units and the length of the base is 8\sqrt{3} units. Let <em>h </em>is the height of the triangle thus by the Pythagoras theorem,

(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2

Solve for <em>h,</em>

<em />

<em />\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end<em />

<em />

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

brainly.com/question/4268382

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