1. what is ad/ab in simplest form
a. 10/3
b. 1/3
c. 17/5
d. 3

what is slope of be/ slope of ae in simplest form?
a. 4
b. 5/4
c. 25/4
d. 5

3. what is the value of x in the proportion (x-1)/5= (4x+2)/35?
a. 1/3
b. 1/5
c. 1/4
d. 3

4. what is the value of x in the proportion
x+1 = 15

x+3 = 21

5. the lengths of the sides of a triangle are in the extended ratio 3 : 10 : 12. the perimeter is 400 cm. what is the length of the longest side in centimeters? ?
a. 16 cm
b. 192 cm
c. 160 cm
d. 48 cm

All the ratios for  all the given questions have their answers as;

1) Option D; 3

2) Option A; 4

3) Option D; 3

4) X = 4

5) Option B; 192 cm

From the given graph, we have the following dimensions;

AB = 3

AC = 5

AD = 9

1) We want to find AD/AB;

From the given dimensions;

AD = 9 and AB = 3.

Thus;

AD/AB = 9/3

AD/AB =3

Option D; 3

2) We want to find the slope of BE/slope of AE;

Formula for slope between two points is;

m = (y₂ - y₁)/(x₂ - x₁)

Thus;

Slope of AE;

m_ae = (5-0)/(4-0)

m_ae =5/4

Slope of BE

m_be = (5-0)/(4-3)

m_be = 5/1

m_be = 5

Thus; slope of BE/Slope of AE is;

M_be/m_ae = 5/(⁵/₄)

M_be/m_ae = 4

Option A; 4

3) We want to find the value of x in the proportion (x - 1)/5 = (4x + 2)/35.

We will cross multiply to get;

35(x - 1) = 5(4x + 2)

35x - 35 = 20x + 10

Rearranging to get;

35x - 20x = 10 + 35

15x = 45

divide both sides by 15 to get;

15x/15 = 45/15

x = 3

Option B; 3

4) We want to find the value of x in the proportion:  (x + 1)/(x + 3) = 15/21

We will cross multiply to get;  

21(x + 1) = 15(x + 3)

21x + 21 = 15x + 45

Rearranging to get;

21x - 15x = 45 - 21

6x = 24

divide both sides by 6 to get;

x = 4  

5) We are told that the lengths of the sides of a triangle are in extended ratio 3:10:12 and that the perimeter is 400 cm.

Thus;

This means the original lengths were all divided by a common number. Let us call this number x. Since perimeter is sum of all sides, then;  

3x + 10x + 12x = 400

25x = 400

Divide both sides by 25 to get;

x = 400/25

x = 16

The longest side =  12 × 16

Longest side = 192 cm

Option B; 192 cm

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