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Elina [12.6K]
3 years ago
13

What is the length of AC?

Mathematics
2 answers:
Elan Coil [88]3 years ago
6 0

well, the triangle is an isosceles, so it twin sides, and the twin sides make twin angles, as we see by the tickmarks on A and C, meaning AB = BC.

\bf x+4=3x-8\implies 4=2x-8\implies 12=2x\implies \cfrac{12}{2}=x\implies 6=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ AC\implies x+4\implies 6+4\implies 10

Temka [501]3 years ago
4 0

Answer : The length of AC is, 6

Step-by-step explanation :

As we know that when the two angles in a triangle are equal then the there adjacent sides are also equal.

That means,

∠A = ∠C

So,

Side AB = Side BC

x + 4 = 3x -8

3x - x = 8 + 4

2x = 12

x = 6

The values of 'x' is 6

So, the length of AC = x = 6

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The quadrilateral is a trapezoid and the area of the quadrilateral is 85.04 square units

<h3>How to determine the quadrilateral?</h3>

The vertices are given as:

A:(-2, 3) B:(4, -6) C:(10, 2) D:(6, 8)

Next, we plot the vertices (see attachment)

From the attached graph, we can see that the quadrilateral is a trapezoid

<h3>How to determine the area?</h3>

From the plot, we have the following features:

Height: AD

Parallel sides: CD and AB

Calculate the lengths using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

So, we have:

AD = \sqrt{(-2 -6)^2 + (3 -8)^2}

AD = \sqrt{89}

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The area is then calculated as:

Area = 0.5 * (CD + AB) * AD

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Area = 0.5 * (√52 + √117) * √89

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Area = 85.04

Hence, the area of the quadrilateral is 85.04 square units

Read more about areas at:

brainly.com/question/24487155

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