(a) x = 6.5 cm
(b) x = 10 cm
(c) x = 7 cm
(d) x = 7.9 cm
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!!