The perimeter of a right triangle …

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The perimeter of a right triangle is 24cm . If its hypotenuse is 10cm . Find its area?

Posted by Nakshathra S 5 years, 2 months ago

CBSE > Class 09 > Mathematics

4 answers

Dj Jd 5 years, 2 months ago

24cm^2

0Thank You

Prashant Jinwal 5 years, 2 months ago

0Thank You

Yogita Ingle 5 years, 2 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 ,

$Area \: of \: \triangle ABC = \frac{1}{2} \times AB \times BC\\=\frac{1}{2}\times xy\\=\frac{1}{2}\times 48$

/* From (3) \

$= 24\: cm^{2}$

Therefore,

$Area \: of \: the\:triangle =24\: cm^{2}$

1Thank You

Manpreet Singh 5 years, 2 months ago

0Thank You

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CBSE > Class 09 > Mathematics