Question

Calculate x for each of the following right angled triangles.

Answer 1

$\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}$

(a) x = 6.5 cm

(b) x = 10 cm

(c) x = 7 cm

(d) x = 7.9 cm

Step-by-step explanation:

To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..

Formula :

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

(h)^2 = (p)^2 + (b)^2

therefore,

(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.

by formula,

→ h^2 = p^2 + b^2

→ (x)^2 = (√12)^2 + (√30)^2

→ x^2 = 12 + 30

→ x^2 = 42

→ x = √42

→ x = 6.480...

→ x = 6.5 cm. (approx)

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(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.

by formula,

→ h^2 = p^2 + b^2

→ (√300)^2 = (x)^2 + (√200)^2

→ 300 = x^2 + 200

→ x^2 = 300 – 200

→ x^2 = 100

→ x = √100

→ x= 10 cm.

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(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.

by formula,

→ h^2 = p^2 + b^2

→ (√66)^2 = (x)^2 + (√17)^2

→ 66 = x^2 + 17

→ x^2 = 66 – 17

→ x^2 = 49

→ x = √49

→ x = 7 cm.

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(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.

by formula,

→ h^2 = p^2 + b^2

→ (x)^2 = (2√3)^2 + (5√12)^2

→ x^2 = 12 + 50

→ x^2 = 62

→ x = √62

→ x = 7.874...

→ x = 7.9 cm. (approx)

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Hope it helps you!!