Question

Ratio of the base and hypotenuse of right angled triangle is 4:5and the perimeter of triangle is 48cm then its area is

Answer 1

$\mathfrak{\huge{Answer:}}$

$\mathbb{GIVEN}$

Base : Hypotnuese = 4 : 5

Perimeter of the triangle = 48 cm

$\mathbb{TO\:FIND}$

The Area of the triangle

$\mathbb{METHOD}$

Let the base and the hypotnuese be = 4x and 5x respectively

According to the Pythagoras Theorem:

$\tt{H^2 = P^2 + B^2}$

Here, Hypotnuese = 5x

Base = 4x

=》 $\tt{P^2 = 25x^2 - 16x^2}$

=》 $\tt{P = \sqrt{9x^2}}$

=》 $\tt{P = 3x}$

Perimeter = Sum of all sides

=》 Perimeter = 4x + 5x + 3x

=》 Perimeter = 12x

=》 Perimeter = 48 cm

=》 48 = 12x

=》 x = 4

The length of the dimensions of the triangle will thus be:

The perpendicular line =》 3x = 12 cm

The base line =》 4x = 16 cm

The hypotnuese line =》 5x = 20 cm

Area of a triangle = $\sf{\frac{1}{2} \times b \times h}$

=》 Area of the triangle = $\sf{\frac{1}{2} \times 16 \times 12}$

=》 Area of the triangle = 96 $cm^2$

Thus, the area will be $\tt{\huge{96\:cm^{2}}}$