Quantitative Aptitude Ques 817
Question: If the perimeter of a right angled triangle is 56 cm and area of the triangle is $ 84cm^{2}, $ then the length of hypotenuse is (in cm)
Options:
A) 25
B) 50
C) 7
D) 24
Show Answer
Answer:
Correct Answer: A
Solution:
- Let a, b and c be the sides of the triangle and 6 is the length of the hypotenuse.
Now, perimeter = 56
$ a+b+c=56 $
Area = 84
$ \Rightarrow $ $ \frac{1}{2}\times ac=84 $
$ \Rightarrow $ $ ac=168 $ By Pythagorus theorem, $ b^{2}=a^{2}+c^{2} $ $ ={{(a+c)}^{2}}-2ac $ $ ={{(56-b)}^{2}}-2\times 168 $
$ \Rightarrow $ $ b^{2}=3136+b^{2}-112b-336 $
$ \Rightarrow $ $ 112b=2800 $
$ \Rightarrow $ $ b=\frac{2800}{112}=25 $
BETA
