Question

Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is x, the length of D C is 4 x, and the length of B D is 10.

What is the value of x?

a. 2 units
b. 3 units
c. 5 units
d. 8 units

Answer 1

C. - X = 5 units

Explanation:

We need to solve for x from the given figure.

In ΔADB and ΔCDB

∠ABD=∠BCD (Corresponding angle of two right triangle)

∠ADB=∠CDB (Each 90°)

∴ ΔADB ≈ ΔCDB By AA similarity

If two triangles are similar then ratio of their corresponding height are same.

Substitute the value of side into the expression

Cross multiply and solve for x

x can't be negative because side of triangle is positive.

Hence, The value of x is 5 units.