Question

find area of triangle

Answer 1

HEY_____MATE

YOUR 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.

Answer 2

Hey mate !!


Hypotenuse given 25cm
Perimeter = 60

Perimeter = sum of sides

=> base + perpendicular + 25 = 60

=> base + perpendicular = 60 - 25

=> base + perpendicular = 35cm

We know that, by Pythagoras theorem

Hypotenuse² = (base² + perpendicular²)

=> (b² + p²) = 25²

=> b² + p² = 625

Also we know that, using identity,


b² + p² = (b + p)² - 2bp
and base + perpendicular = 35 as derived above

=> 625 = (35)² - 2bp

=> 625 = 1225 - 2bp

=> -2bp = 625 - 1225

=> - 2bp = -600

=> bp = 600/2

=> base × perpendicular = 300


Now we know that area of triangle =


1/2 × base × perpendicular (height)

=> 1/2 × 300

=> 150cm²


Your answer 150cm²


Hope it helps dear friend ☺️✌️✌️

Nice question