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nlexa [21]
3 years ago
5

If K is the midpoint of JL, JK = 9x -1 and KL = 2x +27, find JL

Mathematics
2 answers:
alina1380 [7]3 years ago
6 0

Answer:

<h2>JL is 70 units long.</h2>

Step-by-step explanation:

Givens

  • K is the midpoint of JL. Where JL = 11x + 26.
  • JK = KL by midpoint definition.
  • JK = 9x - 1  by given.
  • KL = 2x + 27 by given.

Replacing each expression, we have

JK = KL

9x - 1 = 2x + 27

9x - 2x = 27 + 1

7x = 28

x = 28/7

x = 4

Replacing this value in JL expression.

JL = 11x + 26

JL = 11(4) + 26

JL = 44 + 26

JL = 70 units.

Therefore, JL is 70 units long.

Liula [17]3 years ago
3 0

Answer:

JL = 70

Step-by-step explanation:

Since K is the midpoint of JL then JK = KL and

JL = JK + KL = 9x - 1 + 2x + 27 = 11x + 26

solve for x using JK = KL

9x - 1 = 2x + 27 ( subtract 2x from both sides )

7x - 1 = 27 ( add 1 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4, hence

JL = 11x + 26 = (11 × 4 ) + 26 = 44 + 26 = 70


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<h3><u>Option 1:  The kite area formula</u></h3>

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If you've forgotten why that is the formula for the area of a kite, observe the attached diagram: note that the kite (shaded in) is half of the area of the rectangle that surrounds the kite (visualize the 4 smaller rectangles, and observe that the shaded portion is half of each, and thus the area of the kite is half the area of the large rectangle).

The area of a rectangle is Area_{rectangle}=bh, sometimes written as Area_{rectangle}=bh, where w is the width, and h is the height of the rectangle.

In the diagram, notice that the width and height are each just the diagonals of the kite.  So, the <u>Area of the kite</u> is <u>half of the area of that surrounding rectangle</u> ... the rectangle with sides the lengths of the kite's diagonals.Hence, Area_{kite}=\frac{1}{2} d_{1}d_{2}

For our situation, each of the diagonals is already broken up into two parts from the intersection of the diagonals.  To find the full length of the diagonal, add each part together:

For the horizontal diagonal (which I'll call d1): d_{1}=40m+6m=46m

For the vertical diagonal (which I'll call d2): d_{2}=16m+16m=32m

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Area_{kite}=\frac{1}{2} d_{1}d_{2}\\Area_{kite}=\frac{1}{2} (46m)(32m)\\Area_{kite}=736m^2

<h3><u /></h3><h3><u>Option 2:  The sum of the parts (version 1)</u></h3>

If one doesn't remember the formula for the area of a kite, and can't remember how to build it, the given shape could be visualized as 2 separate triangles, the given shape could be visualized as 2 separate triangles (one on top; one on bottom).

Visualizing it in this way produces two congruent triangles.  Since the upper and lower triangles are congruent, they have the same area, and thus the area of the kite is double the area of the upper triangle.

Recall the formula for area of a triangle:  Area_{triangle}=\frac{1}{2} bh where b is the base of a triangle, and h is the height of the triangle <em>(length of a perpendicular line segment between a point on the line containing the base, and the non-colinear vertex)</em>.  Since all kites have diagonals that are perpendicular to each other (as already indicated in the diagram), the height is already given (16m).

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<h3><u>Option 3:  The sum of the parts (version 2)</u></h3>

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<em>Note:  In this visualization, the two triangles are not congruent, so it is not possible to  double one of their areas to find the area of the kite.</em>

The base of the left triangle is the vertical line segment the is the vertical diagonal of the kite.  We'll need to add together the two segments that compose it:  b=16m+16m=32m.  This is also the base of the triangle on the right.

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<h3><u>Option 4:  The sum of the parts (version 3)</u></h3>

If you don't happen to see those composite triangles from option 2 or 3 when you're working this out on a particular problem, the given shape could be visualized as 4 separate right triangles, and we're still given enough information in this problem to solve it this way.

<u>Calculating the area of the 4 right triangles</u>

Area_{\text{upper left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2

Area_{\text{upper right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2

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Area_{\text{lower right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2

<u>Calculating the area of the kite</u>

Area_{kite}=(320m^2)+(48m^2)+(320m^2)+(48m^2)

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