The area of a right angled triangle...
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The area of a right angled triangle is 40 sq. cm. and its perimeter is 40 cm. The length of its hypotenuse is (a) 16 cm (b) 18 cm © 17 cm (d) Data sufficient

JEE/Engineering Exams
Maths
Solution
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Let ia be the base, ( b^{prime} ) be the height 8 C be the hypotenuse. [ begin{array}{l} text { Area, } frac{1}{2} times a times b=40 Rightarrow a b=80-(1) text { Perimeren, } a+b+c=40 Rightarrow a+b=40-c-(2) end{array} ] for right angle ( Delta ), [ begin{array}{c} a^{2}+b^{2}=c^{2} Rightarrow(a+b)^{2}-2 a b=c^{2} end{array} ] Sabstitusing (1) ( &(2) ) [ begin{array}{l} quad(40-c)^{2}-2 times 80=c^{2} Rightarrow 80 c=1440 Rightarrow text { hypotenute, } underline{c}=18 end{array} ]
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