Question

The ratio between the base and height of a right angled triangle is 4 : 3 respectively, if the hypotenuse is 10 cm., what is the area of the triangle ?

Answer 1

Let the base of the right angled triangle is 4x cm and height of the right angled triangle is 3x cm , given that the hypotenuse of the right angled triangle is 10 cm. We can apply Pythagoras theorem,





$\underline{By \: Pythagoras \: Theorem , } \\ base^{2}+height^{2}= hypotenuse^{2}$

= > ( 4x )² + ( 3x )² = ( 10 )²

= > 16x² + 9x² = 100

= > x² ( 16 + 9 ) = 100

= > x² × 25 = 100

= > x² = 4

= > x = 2




Then,
As this is a right angled triangle,


$Area = \frac{1}{2} \times height \times base$

$= > Area = \frac{1}{2} \times 4x \times 3x \\ \\ \\ = > Area = 2x \times 3x \\ \\ \\ = > Area = 6 {x}^{2} \\ \\ \\ = > Area = 6 {(2)}^{2} \\ \\ \\ = > Area = 6 \times 4 \\ \\ \\ = > Area = 24 \: {cm}^{2}$