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ICSE Class 9 Answered

In a right angle triangle the smaller sides are (x+9) and(3x+3)cm.find its perimeter if it's area is 54cm²
Asked by Siddiquesaif604 | 25 Nov, 2018, 08:44: PM
answered-by-expert Expert Answer
Smaller sides in right-angled triangle means, sides of right angle.
Hence area of right-angled triangle = (1/2)(x+9)(3x+3) = 54 ....................(1)
 
Eqn.(1) is reduced to :-  x2 + 10x - 27 = 0 ....................(2)
 
valid root of the quadratic eqn.(2) is x =  begin mathsize 12px style open parentheses 2 square root of 13 space minus 5 close parentheses space equals space 2.21 end style
sides of right angle are 11.21 cm and 9.63 cm .  Hypotenuse = ( 11.21×11.21 + 9.63×9.63 )0.5 = 14.8 cm
 
Perimeter of triangle = 11.21+9.63+14.80 = 35.64 cm
Answered by Thiyagarajan K | 25 Nov, 2018, 10:48: PM

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