Question

Find all sides of a right triangle whose perimeter is equal to $\:\sf\underline\red{60\:cm}\:$and its area is equal to $\:\sf\underline\purple{150cm^{2}}$​

Answer 1

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

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

hope it helps