If the perimeter of a right-angled isosceles triangle is $$\left( {4\sqrt 2 + 4} \right)$$ cm, the length of the hypotenuse is :
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
Answer: Option A
Solution(By Examveda Team)
Let the length of each of the sides containing the right angle be x cmThen,
Hypotenuse :
$$\eqalign{ & = \sqrt {{x^2} + {x^2}} \,cm \cr & = \sqrt {2{x^2}} \,cm \cr & = \sqrt 2 x\,cm \cr} $$
Perimeter of the triangle :
$$\eqalign{ & = \left( {x + x + \sqrt 2 x} \right)cm \cr & = \left( {2x + \sqrt 2 x} \right)cm \cr & = \sqrt 2 x\left( {\sqrt 2 + 1} \right)cm \cr & \therefore \sqrt 2 x\left( {\sqrt 2 + 1} \right) = \left( {4\sqrt 2 + 4} \right) \cr & \Rightarrow \sqrt 2 x\left( {\sqrt 2 + 1} \right) = 4\left( {\sqrt 2 + 1} \right) \cr & \Rightarrow \sqrt 2 x = 4 \cr & \Rightarrow x = 2\sqrt 2 \cr} $$
Hence, hypotenuse :
$$\eqalign{ & = \left( {\sqrt 2 \times 2\sqrt 2 } \right)cm \cr & = 4\,cm \cr} $$
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A. 15360 m2
B. 153600 m2
C. 30720 m2
D. 307200 m2
E. None of these
A. 2%
B. 2.02%
C. 4%
D. 4.04%
E. None of these
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B. 18 cm
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D. Data inadequate
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The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A. 40%
B. 42%
C. 44%
D. 46%
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