Question

if area of a right angle traingle 216m and the base is 24m find the perimeter of triangle

Answer 1

xy/2 = 216, or

xy = 432 …(1)

The hypotenuse = (x^2+y^2)^0.5. The perimeter

72 = x + y + (x^2+y^2)^0.5, or

(x^2+y^2)^0.5 = 72 -x-y. Squaring both sides

x^2+y^2 = (72 -x-y)^2 = 5184 + x^2 + y^2 - 144x - 144y + 2xy, or

5184 - 144x - 144y + 2xy = 0 …(2). Put xy = 432 from (1) on (2) to get

5184 - 144x - 144y + 2*432 = 0, or

6048 - 144x - 144y = 0

42 - x - y = 0

Therefore, the sum of the lengths of perpendicular sides = 42 cm.

Check: x + y = 42. Or y = 42-x

xy/2 = 216

(42-x)x = 432, or

x^2 - 42x + 432 = 0

(x-24)(x-18) = 0

Hence the two perpendicular sides are 24 cm and 18 cm, and the hypotenuse = (24^2+18^2)^0.5=(576+324)^0.5 = 900^0.5 = 30 cm.

Check: Perimeter = 24+14+30 = 72 cm.

Area = 24*18/2 = 216 sq cm.

Answer 2

Hope this pic will help u..