Question

if the base of a right angled triangle is 15 CM and it's hypotenuse is 25 CM then find it's area (by heron's formula) ​

Answer 1

Answer:

150

Step-by-step explanation:

typing take too much time

Answer 2

Answer : 150 cm²

$\rule{100}2$

Step - By - step Explanation :

In a Δ,

• hypotenuse side = 25 cm
• Base = 15 cm

We have to find it's area.

In order to find it's area, it is necessary to find it's perpendicular side.

We know that,

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

Substitute the given values.

we get,

$\sf {25}^2 = {P}^2 + {15}^2$

$\sf\implies {625} = {P}^2 + {225}$

$\sf\implies {P}^2 = 625 - 225$

$\sf\implies {P}^2 = 400$

$\sf\implies P=\sqrt{400}$

$sf\therefore P = 20$

Now,

$\sf S = \dfrac{25+15+20}{2}$

$\sf S = \dfrac{60}{2}$

$\sf S = 30$

We know that,

Area of Δ $\sf = \sqrt{S(S-side_1)(S-side_2)(S-side_3)}$

$\sf = \sqrt{30(30-25)(30-15)(30-20)}$

$\sf = \sqrt{30(5)(15)(10)}$

$\sf = \sqrt{3\times 10\times 5\times 3\times 5\times 10}$

$\sf = 3\times 10\times 5$

$\sf = 30\times 5$

$\sf = 150$

Hence,

Area of the given triangle is 150 cm².

$\rule{200}2$