Question

The perimeter of a right triangle is 144 cm and its hypotenuse measures 65
cm. Find the length of other sides and calculate its area.

Pls answer asap

Answer 1

Step-by-step explanation:

Answer:

The result can be verified using Herons formula as follows:

Step-by-step explanation:

Step 1:

Let the two sides are x and y.

x^{2}+y^{2}=652x

2

+y

2

=652

Perimeter of right angled triangle is 144 cm.

Step 2:

So we get

And x + y + 65 = 144

x + y = 144 - 65 = 79

Step 3:

Squaring both sides, we get

\begin{gathered}\begin{aligned}(x+y)^{2} &=79^{2} \\ \Rightarrow x^{2}+y^{2}+2 x y &=6241 \end{aligned}\end{gathered}

(x+y)

2

⇒x

2

+y

2

+2xy

=79

2

=6241

4225 + 2 x y = 6241

2 x y = 6241 – 4225

2 x y = 2016

x y = 2016 / 2

x y = 1008

y = 1008 / x

Step 4:

Sub:

y = 1008 / x in x + y = 79, we get

x + 1008 / x = 79

x^2x

2

+ 1008 = 79 x

x^2x

2

- 79 x +1008 = 0

x^2x

2

- 63 x - 16 x + 1008 = 0

x ( x - 63 ) - 16 ( x - 63 ) = 0

( x - 63 ) ( x - 16 ) = 0

So, x = 63 cm or x = 16 cm

Step 5:

The length of other sides are 63 cm, 16 cm.

Area of right angled triangle is

1 / 2 x 63 x 16 = 504 \mathrm{cm}^{2}504cm

2

Step 6:

Verify the result using Heron's Formula

S = ( 16 + 63 + 65 ) / 2 = 72

A = ( s x ( s-a ) x ( s - b ) x ( s - c ) )1/2

= ( 72 x (72 - 16 ) x ( 72 - 63 ) x ( 72 - 65 ) )1/2

= ( 72 x 56 x 9 x 7 ) 1/2

= ( 9 x 8 x 8 x 7 x 9 x 7 )1/2

A = 9 x 8 x 7 = 504 \mathrm{cm}^{2}504cm

2