Question

Hello I need help on this question!

Answer 1

Answer:

5

Step-by-step explanation:

Refer to attachment for marking of sides.

In the given figure , ∆ABC , ∆ABD and ∆ADC are right angled triangles . Therefore here we can use the Pythagoras theorem , as ,

$\longrightarrow$ base² + perpendicular² = hypotenuse ² .

• In ∆ABD , we have ;

$\longrightarrow$ AB² + BD² = AD²

$\longrightarrow$ AB² + x² = 10²

$\longrightarrow$ AB² = 10² - x²

$\longrightarrow$ AB² = 100 - x²

$\rule{200}2$

• Again in ∆ADC , we have ;

$\longrightarrow$ AC² + AD² = CD²

$\longrightarrow$ AC² = 20² - 10²

$\longrightarrow$ AC² = 400 - 100

$\longrightarrow$ AC² = 300

$\rule{200}2$

Again in ∆ABC , we have ,

$\longrightarrow$ AC² = AB² + BC²

Substituting the values from above ,

$\longrightarrow$ 300 = 100-x² + (20-x)²

$\longrightarrow$ 300 = 100 - x² + 400 + x² - 40x

$\longrightarrow$ 40x = 500 - 300

$\longrightarrow$ 40x = 200

$\longrightarrow$ x = 200/40

$\longrightarrow$ x = 5

Hence the required answer is 5 .