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# How do you work out the perimeter and interior angles of a right angle triangle when its height is 7.04 cm greater than its base and has an area of 297.3696 square cm?

Updated: 12/20/2022

Wiki User

13y ago

First the height and base of the triangle must be found so let the height be (x+7.04) and the base be x:-

1/2*height*base = area

1/2*(x+7.04)*x = 297.3696 cm2

Multiply both sides by 2 and multiply out the brackets:

x2+7.04x = 594.7392

Subtract 594.7329 from both sides thus forming a quadratic equation:

x2+7.04-594.7392 = 0

Solving the above by means of the quadratic equation formula gives x a positive value of 21.12

Therefore: height = 28.16 cm and base = 21.12 cm

Use Pythagoras' theorem to find the third side which will be the hypotenuse:

28.162+21.122 = 1239.04 and the square root of this is 35.2

Therefore the perimeter = 28.16+21.12+35.2 = 84.48 cm

Use any of the trigonometrical ratios to find the interior angle:

tan-1(28.16/21.12) = 53.13010235 or 53 degrees to the nearest degree

Therefore the interior angles are 53 degrees, 37 degrees and 90 degrees

Wiki User

13y ago