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Sunny_sXe [5.5K]
3 years ago
11

Given the overlapping triangles shown at the right. Notice the parallel segments. Find x. 6 х 9 MathBils.com 20​

Mathematics
1 answer:
Nat2105 [25]3 years ago
4 0

Using the principle of parallel lines, the value of x in the given triangle is calculated to be 8

<u>The</u><u> </u><u>smaller</u><u> </u><u>triangle</u><u> </u><u>can be</u><u> </u><u>expressed</u><u> </u><u>as</u><u> </u><u>:</u>

  • Side / base = 6/x ----(1)

<u>The</u><u> </u><u>larger</u><u> </u><u>triangle</u><u> </u><u>can</u><u> </u><u>be</u><u> </u><u>expressed</u><u> </u><u>as</u><u> </u><u>:</u>

  • Side / base
  • Side = 6+9 = 15
  • 15/20 - - - - - (2)

<u>Equating</u><u> </u><u>(</u><u>1</u><u>)</u><u> </u><u>and</u><u> </u><u>(</u><u>2</u><u>)</u><u> </u><u>:</u>

6/x = 15 / 20

15x = 20 × 6

15x = 120

x = 120 / 15

x = 8

Therefore, the value of x in the triangle is 8.

Learn more : brainly.com/question/25326255

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14. The area of a rectangle is 375 square inches and it’s perimeter is 80 inches. Find both the length and width.
Pavel [41]

Answer:

Length  =25 inches

Width = 15 inches

Step-by-step explanation:

Let l = length of rectangle, w = width of rectangle

Given the area and the perimeter of the rectangle, we can write:

lw = 375

2l+2w=80

So:

l+w = 80\div2

=40

l=40-w

Now, we can use substitution to find the value of w:

lw = 375

(40-w)w = 375

40w-w^2 = 375

375+w^2-40w = 0 (Quadratic equation)

(w-15)(w-25) = 0

∴ w = 15, 25

We can use substitution again to find the value of l

lw = 375

l=375\div w

=25,15

∵ Length usually refers to the longer side of a rectangle, ∴ length =25 inches and width =15 inches.

Hope this helps :)

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