Question

Let ABC be a right triangle with length of side AB=3 and hypotenuse AC=5.If D is a point on BC such that BD/DC=AB/AC, then AD is equal to?

Answer 1

Hope it's clear.
Any doubts, comment.

Answer 2

Therefore the length of AD is 3.35 units.

Given:

ABC be a right triangle with a length of side AB=3 and hypotenuse AC=5.

If D is a point on BC such that BD/DC=AB/AC.

To Find:

The length of AD =?

Solution:

This question of the right-angled triangle can be solved in this way.

In ΔABC, By using Pythagoras theorem

⇒ AC² = AB² + BC²

⇒ 5² = 3² + BC²

⇒ 25 = 9 + BC²

⇒ BC = √16 = 4

∴ The length of BC = 4 units

Now,  BD/DC=AB/AC

⇒ BD/DC=3/5

Let BD = 3x and DC = 5x then BC = 8x

But we know that BC = 4 units

⇒ 8x = 4 ⇒ x = 0.5

Then, BD = 3x = 3 × 0.5 = 1.5 units and DC = 5x = 5 × 0.5 = 2.5 units { Look at the image attached for better understanding }

Now ABD is also a right-angled triangle.

In ΔABD, By using Pythagoras theorem

⇒ AD² = BD² + AB²

⇒ AD² = 1.5² + 3²

⇒ AD² = 2.25 + 9 = 11.25

⇒ AD = √11.25 = 3.35

Therefore the length of AD is 3.35 units.

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