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

1.	The perimeter of a right triangle is 24cm . If its hypotenuse is 10cm . Find its area?
Answer» 24cm^2 20 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(\xa0From (2) ]=> 2xy = 196-100=> 2xy = 96Divide 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} 20

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