Question

Find the value of x.All measurements are in centimeters.​

Answer 1

In ∆ABC,

given :-

» AB = 12cm (height)

» AC = 13cm (hypotenuse)

» BC = ? (base)

by Pythagoras theorem, we get

➡ hypotenuse² = height² + base²

➡ 13² = 12² + base²

➡ 169 = 144 + base²

➡ 169 - 144 = base²

➡ 25 = base²

➡ base = √25 = 5cm

therefore BC = 5cm

in ∆CDE,

given :-

» CD = 10cm (hypotenuse)

» DE = 6cm (height)

» CE = ? (base)

again using Pythagoras theorem,

➡ hypotenuse² = height² + base²

➡ 10² = 6² + base²

➡ 100 = 36 + base²

➡ 100 - 36 = base²

➡ 64 = base²

➡ base = √64 = 8cm

therefore CE = 8cm

now, we've to find the value of x

x = BC + CE

➡ x = 5 + 8

➡ x = 13cm

hence, the value of x = 13cm

refer to the attachment for the figure.

Answer 2

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⇒13 cm

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Breaking into two different triangles

∆ABC & CDE

In ∆ABC

Using Pythagorous

BC² = AC² - AB²

⇒BC² = (13)² - (12)²

⇒BC = 5

Similarly

In ∆CDE

CD² = CE² - DE²

⇒CD² = (10)² - (6)²

⇒CD = 8

⇒BC + CD = BD = x = 5 + 8 = 13 cm