Question

the perimeter of a right triangle is 60cm its hypotenuse is 25cm find the area of triangle

Answer 1

Answer:

Step-by-step explanation:

Perimeter of that triangle = 60cm

the measure of hypotenuse = 25cm

then the rest sides must measure = 60-25

= 35

let one side be x

then, the 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

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

★ Given :

Perimeter of right triangle is 60 cm.

Hypotenuse is of 25 cm.

★ Solution :

Let one side of the right triangle be x cm.

So, another side will be = 60 - 25 - x = 35 - x cm

Now,

By Pythagorean theorem

$\Large{\boxed{\red{\sf{Hypotenuse^2 = Perpendicular^2 + Base2}}}}$

(Putting Values)

(25)² = x² + (35 - x)²

Using identity

$\Large{\boxed{\green{\sf{(a + b) ^2 = a^2 + b^2 + 2ab}}}}$

625 = x² + 1225 + x² - 70x

⟹ x² + x² - 70x + 1225 - 625 = 0

⟹ 2x² - 70x + 600 = 0

⟹ 2x² - 40x - 30x + 600 = 0

⟹ 2x(x - 20) -30(x - 20) = 0

⟹ (2x - 30) (x - 20) = 0

Now,

x - 20 = 0

x = 20

____________________

Or

2x - 30 = 0

2x = 30

x = 30/2

x = 15

____________________

When x = 15

Then Base is 20 cm and perpendicular is 15 cm.

When x = 20

Then base is 15 cm and perpendicular is 20 cm.

____________________

I'm both the cases we get the measure of two sides as 15 cm and 20 cm.

Now,

We know the area of triangle

$\Large{\boxed{\orange{\sf{Area = \frac{1}{2} \times Base \times Height}}}}$

(Putting Values)

$\sf{ \implies \: area \: = \frac{1}{ \cancel{2}} \times 15 \times \cancel{20}} \\ \\ \sf{ \implies \: area \: = \: 150 \: {cm}^{2} }$

$\Large{\boxed{\blue{\sf{Area = 150 \: cm^2}}}}$