Question

Please solve the problem

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Answer 1

Answer: xiii: x=4 xiv: x=5 y=11

Explanation:

Ok, for xiii, there is a ratio.

BD:DC aka 3:x You're trying to solve for x (DC)

On the other side of the equation, it's AB:AC aka 6:8 This ratio can be simplified to 3:4 (when you divide both sides by 2)

To set things up:

3:x = 3:4

Notice the similarity? Since they are equal to one another, x must be 4.

Now for xiv, you're trying to find the values of x and y.

DE=3 and AB=x+1

DE=1/2 of AB

so,

3=(x+1)/2 Solving for x, multiply both sides by 2

6=x+1 subtract both sides by 1

-1 -1

x=5

If you plug x to AB, AB = 6

Plug x to BE = 4

To find y, notice how there is a dash that marks them as congruent, so the lengths BE and EC must be equal.

so y-7=4 (adding 7 to both sides)

+7 +7

y=11

Answer 2

See below ~

Explanation:

Section (xiii) :

• m(AB) : m(AC) = m(BD) : m(DC)
• 6 : 8 = 3 : x
• 6/8 = 3/x
• x = 3/6 x 8
• x = 0.5 x 8
• x = 4

Section (xiv) :

• DE = 1/2(AB)
• 3 = 1/2(x + 1)
• x + 1 = 6
• x = 5

It is indicated in the diagram that CE = EB :

• y - 7 = x - 1
• y = 5 - 1 + 7
• y = 12 - 1
• y = 11