Question

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find the value of x

Answer 1

Answer:

           x = √70

Step-by-step explanation:

From ΔABD:

                   BD² + 7² = x²   ⇒  BD² = x² - 49

Form ΔBCD:

                   BD² + 3² = BC²   ⇒  BD² = BC² - 9

so:

       BC² - 9 = x² - 49   ⇒  BC² = x² - 40

From ΔABC:

                 x² + BC² = (7+3)²

                  x² + x² - 40 = 10²

                   2x² = 140

                    x² = 70

                    x = √70                    

Answer 2

Answer:

x = $\sqrt{70}$

Step-by-step explanation:

Δ ABC and Δ ADB are similar, thus ratios of corresponding sides are equal, that is

$\frac{AB}{AD}$ = $\frac{AC}{AB}$ ( cross- multiply )

AB² = AC × AD = 10 × 7 = 70 ( take the square root of both sides )

AB = x = $\sqrt{70}$