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A right angle triangle ABC whose area is 84 cm2. The sum of perpendicular and base of triangle ABC is 31,then find the hypotenuse of triangle 

A right angle triangle ABC whose area is 84 cm2. The sum of perpendicular and base of triangle ABC is 31,then find the hypotenuse of triangle  Correct Answer 25 cm 

Given 

Area of triangle = 84 cm2

Formula Used 

H2 = P2 + B2

Area of triangle = 1/2 × P × B

Calculation 

Area of triangle = 1/2 × P × B 

⇒ 84 = 1/2 × P × B 

⇒ PB = 168 cm2 

(P + B) = 31 

squaring both side 

⇒ P2 + 2PB + B2 = 312 

⇒ P2 + B2 = 961 - 168 × 2 = 625 

⇒ H2 = 625 

⇒ H = 25 cm 

∴ The hypotenuse is 25 cm 

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