Question

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}
]

# 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

Solution