Определите AB если AD=9см AC=16см CD высота CDA=90°

AB = 7 cm.

To find the length of segment AB, we can use the Pythagorean theorem.

Since triangle CDA is a right-angled triangle with a 90° angle at vertex D, we can apply the theorem:

AD^2 + CD^2 = AC^2

Substituting the given values:

9^2 + CD^2 = 16^2

Solving for CD^2:

CD^2 = 16^2 - 9^2 CD^2 = 256 - 81 CD^2 = 175

Taking the square root of both sides:

CD ≈ √175

CD ≈ 13.23 cm

Now, we can use CD as the height of the triangle.

Since CDA is right-angled, we can apply the formula for the area of a right-angled triangle:

Area = (1/2) * AB * CD

Substituting the known values:

Area = (1/2) * AB * 13.23

Given that the area of CDA is equal to half the product of AB and CD, and the area is 0.5 * AD * AC, we can set up the equation:

(1/2) * AB * 13.23 = 0.5 * 9 * 16

Simplifying:

AB * 13.23 = 72

Dividing both sides by 13.23:

AB ≈ 5.45 cm

So, AB is approximately equal to 5.45 cm.