What is the area of the right angled triangle?

I. Height of the triangle is three-fourth of the base.

II. Hypotenuse of the triangle is 5 metres.

From statements I and II,

Let the base of the triangle be

x meter.

$herefore$ Height =$frac{{3x}}{4}$ meter

$sqrt {{ m{Bas}}{{ m{e}}^2} + { m{Heigh}}{{ m{t}}^2}} = ;{ m{Hypotenuse}}$

$Rightarrow sqrt {{x^2} + {{left( {frac{{3x}}{4}} ight)}^2}} = 5 Rightarrow sqrt {{x^2} + frac{{9{x^2}}}{{16}}} = 5$

$Rightarrow sqrt {frac{{16{x^2} + 9{x^2}}}{{16}}} = 5 Rightarrow sqrt {frac{{25{x^2}}}{{16}}} = 5$

$Rightarrow frac{{5x}}{4} = 5$

$Rightarrow x = frac{{4 imes 5}}{5} = 4$

$herefore$ Base = 4 meter and height = $frac{{3 imes 4}}{4} = 3$ meter

$herefore$ Area of right angled triangle $= frac{1}{2} imes 4 imes 3 = 6{{ m{m}}^2}$