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The perimeter of a right triangle is 550m. If its sides are in the ratio 12 : 11 : 7. Find the area of the triangle.
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BRAINLIEST !! BRAINLIEST !!
The perimeter of a right triangle is 550m. If its sides are in the ratio 12 : 11 : 7. Find the area of the triangle.
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Verified answer
GiveN :-
The perimeter of a right triangle is 550 m.
Its sides are in the ratio 12 : 11 : 7.
TO DeterminE :-
The area of the triangle.
AcknowleedgemenT :-
Let the sides of the triangle be 12x, 11x and 7x.
Perimeter of the triangle = sum of all the sides
Area of the triangle = 1/2 × Base × Height
(Hypotenuse)² = (Perpendicular)² + (Base)²
(in a right angle triangle only)
SolutioN :-
Perimeter of the triangle = 12x + 11x + 7x = 550 cm
⇒30x = 550
⇒x = 550/30
⇒x = 55/3
Now, the sides are :-
We know,
in a right angle triangle, the hypotenuse is the longest side. Out of all the sides obtained, 220 is the longest length.
(Refer to the attachment for the diagram)
Let the other 2 sides be considered as base and perpendicular(height).
Now,