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]2 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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