Question

The perimeter of aright angled triangle is 60 cm . it's hypotenuse Is 25 cm.find the area of the triangle

Answer 1

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here is ur answer ➖➖➖➖➖➖➖➖➖➖➖➖➖⬇

Perimeter of that triangle = 60cm

the measure of hypotaneous = 25cm

then the rest sides must measure = 60-25
= 35


let one side be x
then, thw measure of the third side must be 35 - x


using pythagoras theorem

(25)^2 =(x)^2 + (35-x)^2
625 = x^2 + x^2 - 70x + 1225

x^2 + x^2 - 70x + 1225 = 625

x^2 + x^2 - 70x + 1225 -625 = 0


2 x^2 - 70x + 600 = 0
2x^2 - 40x - 30 x + 600= 0
2x (x-20) -30 ( x - 20) = 0
(x-20)(2x-30)=0


x -20 = 0
x = 20

2x -30 =0
2x =30
x = 15


so,
one of the side measure either 20 cm 15 cm

if one side measure 20cm then the other must measure 35 -20 = 15cm

and if it measured 15 cm then the other side measure 35-15 = 20 cm


so,
we will get 20cm and 15 cm as our remaining sides.

one of then will be height and the other misy be the base,
now apply the formula of area of triangle i.e
(1/2) (height)(base)
= (1/2 )(20)(15)

= 150 cm^2


so, the area of that triangle will be 150 cm^2.


hope it helps you...

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Answer 2

Let the other two sides be x and y

So given that perimeter = 60 cm

=> x + y + 25 = 60

=> x + y = 60 - 25

=> x + y = 35 ....................( 1 )


Now by Pythagoras Theorem,

x² + y² = 25²

=> x² + y² = 625.................( 3 )


Now, in equation 1, square both the sides


=> (x + y)² = (35)²

=> x² + y² + 2xy = 1225

put the value of x² + y²

=> 625 + 2xy = 1225

=> 2xy = 1225 - 625

=> 2xy = 600

=> xy = 600/2

=> xy = 300

We have to find the area. We know that area of a triangle

= 1/2 × base × height

Since, it's a right angles triangle, the base and its height would be its other two sides.

=> area =
$\frac{1}{2} \times x \times y \\ \\ = > area = \frac{xy}{2}$

xy = 300

=> area = 300/2

=>area = 150 cm²