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tino4ka555 [31]
3 years ago
8

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
Mathematics
1 answer:
Anika [276]3 years ago
3 0

Answer:

C. - X = 5 units

Step-by-step 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.

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<em>Additional comment</em>

You can reject the first two answer choices immediately, because they are odd. Each face will have an area that is the product of integers, so will be an integer. There are two faces of each size, so <em>the total area of this figure must be an even number</em>.

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