Question

In the figure, angle ABC and angle ADB are each right angles. Additionally, AC = 17.8 units and AD = 5 units. What is the length of segment DB?

Answer 1

Answer:

DB = 8

Step-by-step explanation:

Δ ADB and Δ BDC are similar so ratios of corresponding sides are equal, that is

$\frac{DB}{DC}$ = $\frac{AD}{BD}$ , substitute values

$\frac{DB}{17.8-5}$ = $\frac{5}{BD}$

$\frac{DB}{12.8}$ = $\frac{5}{BD}$ ( cross- multiply )

DB² = 64 ( take the square root of both sides )

DB = $\sqrt{64}$ = 8

Answer 2

The length of segment DB is 8 units.

From the given right triangle we can deduce the following;

• triangle ABD and triangle DBC are similar triangles
• length AC = 17.8 units
• length AD = 5 units

From the corresponding triangle rules, we can calculate the length of DB by considering the following ratios;

$\frac{DB}{DC} = \frac{AD}{DB} \\\\DB^2 = AD\times DC\\\\DB^2 = 5 \times (17.8-5)\\\\DB^2 = 5 \times 12.8\\\\DB^2 = 64\\\\DB = \sqrt{64} \\\\DB = 8 \ units$

Thus, the length of segment DB is 8 units.

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