Question

Hello I need help on this question!

Answer 1

5

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 .