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The perimeter of a right-angled triangle is 24 cm and its area is 24 cm2, if the
hypotenuse is 10 cm, find the remaining sides.
Answers
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GIVEN :-
The Perimeter of a Right-angled Triangle is 24cm.
Hypotenuse is 24cm
Area = 24cm^2
TO FIND :- The remaining sides
SOLUTION
If sum of 3 sides = 24cm
and hypotenuse is 10cm
Then the sum of the remaining sides will be
24 cm - 10 cm = 14cm
Let one of the remaining side be y
The other side Will be 14 - y
According to The Question
Area = 1/2 × Base × Height
=> 24 = 1/2 × y × (14 - y)
=> 48 = y(14 - y)
=>14y - y^2 - 48 = 0
=> y^2 - 14y + 48 = 0
=> y^2 - 6y - 8y + 48 = 0
=> y (y - 6) - 8(y - 6) = 0
=> (y - 6)(y - 8) = 0
=> y = 6 or y = 8
If y = 6 other side Will be 14 - 6 = 8cm while if other will be 8 and that will be 14 - 8 = 6cm.
Hence, the other two sides of the Triangle will be 6cm and 8cm.
VERIFICATION
Hypotenuse ^2 = Base^2 + Height^2
=> 10^2 = 8^2 + 6^2
=> 100 = 64 + 36
=> 100 = 100
Hence, LHS = RHS Our Answer is correct.
And Area = 1/2 × Base × Height
=> 24 = 1/2 × 6 × 8
=> 24 = 3 × 8
=> 24 = 24
Hence, LHS = RHS Our Answer is correct