If the difference between the two sides of a right-angled triangle is $2 c m$ and the area of the triangle is $24 c m^{2};$ find the perimeter of the triangle.

24

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36

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Solution

The correct option is A $24$ cm
Let one side $= a$ , other side $= b$
Given, difference between sides, $a - b = 2$
$∴ b = a - 2$
Area of triangle $= \frac{a (a - 2)}{2} = 24$
$a^{2} - 2 a = 48$
$a = 8, a = - 6$
$c = \sqrt{8^{2} + 6^{2}} = \sqrt{64 + 36} = \sqrt{100} = 10$
$∴ c = 10$
$∴$ perimeter of triangle $= 10 + 8 + 6 = 24$ cm

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If the difference between the two sides of a right-angled triangle is 2cm and the area of the triangle is 24cm2; find the perimeter of the triangle.

The correct option is A 24 cmLet one side =a, other side =bGiven, difference between sides, a−b=2∴b=a−2Area of triangle =a(a−2)2=24a2−2a=48a=8,a=−6c=√82+62=√64+36=√100=10∴c=10∴ perimeter of triangle =10+8+6=24 cm

If the difference between the two sides of a right-angled triangle is $2 c m$ and the area of the triangle is $24 c m^{2};$ find the perimeter of the triangle.