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3 years ago

In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.

Mathematics

1 answer:

krek1111 [17]3 years ago

8 0

Answer:

AC = 14 sqrt(2) = 19.80

Step-by-step explanation:

Below is the diagram showing you how this has been set up. The figure is a trapezoid which means BC and AD are parallel. AC is a transversal of the parallel lines.

Givens

<ABC = <ACD
ABCD is a trapezoid
BC = 14
AD = 28
AC is a transversal of BC and AD

Solution

<ABC = <ACD Given
<DAC = <ACB Alternate interior angles.
ΔACB ≅ΔDAC AA
<BAC = <ADC Angles of similar triangles are equal
AC /28 = 14/AC Form a proportion from corresponding sides
AC*AC = 14 * 28 Cross multiply the proportion. Combine
AC^2 = 392 Express as prime factors.
AC^2 = 7*7*2*2*2 Take the square root of both sides
sqrt(AC)^2 = sqrt(7*7*2*2*2)
AC = 7*2 * sqrt(2)
AC = 14 sqrt(2) = 19.80

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3 years ago

The Garden Task

Igoryamba

If the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

the perimeter = 24 ft
the area = 36 sq. ft
if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Recall:

A square has equal side lengths
Perimeter of a square = 4(side length)
Area of a square = $(side $ length)^2$

Given:

Perimeter of square (P) = $(14x - 32) $ ft$

Side length (s) = $(x + 2) $ ft$

First, let's find the value of x by creating an equation using the perimeter formula:

Perimeter of a square = 4(side length)

Plug in the values

$(14x - 32) = 4(x + 2)$

Solve for x

$14x - 32 = 4x + 8\\\\14x - 4x = 32 + 8\\\\10x = 40\\\\x = 4$

Find how much fencing would be needed (Perimeter of the fence):

Perimeter of the fence = $(14x - 32) $ ft$

Plug in the value of x

Perimeter of the fence = $14(4) - 32 = 24 $ ft$

Find the area of the garden:

Area of the garden = $(side $ length)^2$

Area = $(x + 2)^2$

Plug in the value of x

Area = $(4 + 2)^2 = 6^2 = 36 $ ft^2$

Find the perimeter if the garden size is doubled:

Perimeter of the new garden = 2 x 24 = 48 ft

Find the area if the garden size is doubled:

Perimeter of the new garden = 2 x 36 = 72 sq. ft

In summary, if the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

the perimeter = 24 ft
the area = 36 sq. ft
if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Learn more here:

brainly.com/question/13511952

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2 years ago

At an art auction, Giannina's painting sold for over $300. Write an inequality that describes P, the price of Geannina's paintin

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We are given : Giannina's painting sold for over $300.

Let the price of Geannina's painting in dollars = P.

Note: We are given a word " over " in above statement.

Over word represents more than. So, we need to use more than inequality symbol to write an inequality for the given statement.

Let us rephrase the given statement.

" Price P is greater than $300".

Now, we can write an inequality :

P> 300.

<h3>Therefore, the required inequality for given statement is P > 300.</h3>

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

we know that

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d minus 5-----> (d-5)

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