The perimeter of a right triangle …
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Posted by Nakshathra S 5 years, 10 months ago
- 4 answers
Yogita Ingle 5 years, 10 months ago
Let ABC is a right angled triangle.
i) Perimeter of ∆ABC = 24
=> x+y+10=24
=> x+y = 24-10
=> x+y = 14 ---(1)
ii) By Phythagorean theorem:
AC²= AB²+BC²
=> 10²= x² + y²
=> x²+y² = 100 ---(2)
iii) On Squaring equation (1), we get
=> (x+y)² = 14²
=> x²+y²+2xy = 196
=> 100+2xy = 196( From (2) ]
=> 2xy = 196-100
=> 2xy = 96
Divide both sides by 2 , we get
=> xy = 48 ---(3)
Now ,
{tex}Area \: of \: \triangle ABC = \frac{1}{2} \times AB \times BC\\=\frac{1}{2}\times xy\\=\frac{1}{2}\times 48{/tex}
/* From (3) \
{tex}= 24\: cm^{2}{/tex}
Therefore,
{tex}Area \: of \: the\:triangle =24\: cm^{2}{/tex}
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Dj Jd 5 years, 10 months ago
0Thank You