B is the midpoint of AC and d is the midpoint of ce BD = 3x, and AE = 60. Find the length of AB if AC = 5x + 10.

Mathematics

2 answers:

ratelena [41]2 years ago

8 0

Ab=30 with a scale factor of 2:1

Cloud [144]2 years ago

3 0

Answer:

The length of AB is 30 units.

Step-by-step explanation:

Given B is the midpoint of AC and D is the midpoint of CE.

BD = 3x, AE = 60 and AC = 5x + 10

we have to find the value of AB.

As B is the mid point of AC and D is the mid-point of CE.

By mid-point formula, the length of line joining the mid-points of two sides of triangle is half of the parallel side.

∴ $BD=\frac{1}{2}AE$

⇒ $3x=\frac{1}{2}\times 60$

⇒ $x=10units$

As, B is the mid-point of AC

⇒ $AB=\frac{1}{2}AC=\frac{1}{2}(5x+10)=\frac{1}{2}(5(10)+10)=30units$

The length of AB is 30 units.

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