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Answers
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
Answer:
The length of other sides is 63 cm,16cm
Step-by-step explanation:
The area is 504 cm^2.