Find the length of ae if bd ae and bd is a midsegment of ace

AE = 9 units

Explanation:

We know that the line joining two midpoints in a triangle is parallel to the third side and equals half its length

In the diagram, we are given that:

segment BD // segment AE and that segment BD is a mid-segment of the ΔACE

According the above theorem, we can conclude that:

BD = 0.5 × AE ......................> I

1- getting the length of BD:

Length of segment BD can be calculated using the distance formula:

We are given that:

B is at (3.5,1.5) which means that x₁ = 3.5 and y₁=1.5

D is at (-1,1.5) which means that x₂=-1 and y₂=1.5

Substitute in the formula:

units

2- getting the length of AE:

using equation I:

BD = 0.5 × AE

4.5 = 0.5 × AE

AE = 2 × 4.5

AE = 9 units

Hope this helps :)

45 years old

Step-by-step explanation:

In this question, we have the present ratios of two cousins. Given their ratios is the next five years, we are asked to calculate what the age of Jingjin who is one of the cousins would be in the next five years.

Now, let’s look at their present ratio;

4:7

or we can just say let Jinngjin’s age be j and his cousin’s c presently

4:7 = j:c

4/7 = j/c

4c = 7j •••••••(i)

now in the next five, their ratio will be 3 to 5

mathematically, that is expressed as;

j+5:c+5 = 3:5

(j+5)/(c+5) = 3/5

5(j+5) = 3(c+5)

5j + 25 = 3c + 15

3c - 5j = 10. •••••(ii)

From 2 we can say c = (10+5j)/3

let’s put this into 1, we have;

4[(10+5j)/3] = 7j

40 + 20j = 21j

j = 40

In the next 5 years , j will be 40 + 5 = 45 years old