The perimeter of an isosceles triangle is 32cm. the ratio to the equal side and base is 3:2 . what is the area of the triangle???
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Let the length of the equal sides be "a".
Then, perimeter = a + a + (3/2)*a
But the perimeter is 32cm. Therefore,
32 = 2a + 3a/2 = (4a + 3a)/2 = 7a/2
Therefore a = 32 * 2 / 7 = 9.14 cm.
The equal sides are 9.14 and the base is (3/2)*9.14 = 13.71 cm.
To find the height, we will have to use Pythagoras theorem with the hypotenuse being 9.14 and base being 13.71/2 = 6.855.
Then, the height = sqrt (9.14^2 - 6.855^2) = sqrt [(9.14+6.855)*(9.14-6.855)] = sqrt(15.995*2.285) = 6.05cm
Therefore, area of the triangle = (1/2)*6.05*13.71 = 41.47 sq. cm.
Thus, area of the triangle is 41.47 sq. cm.
Then, perimeter = a + a + (3/2)*a
But the perimeter is 32cm. Therefore,
32 = 2a + 3a/2 = (4a + 3a)/2 = 7a/2
Therefore a = 32 * 2 / 7 = 9.14 cm.
The equal sides are 9.14 and the base is (3/2)*9.14 = 13.71 cm.
To find the height, we will have to use Pythagoras theorem with the hypotenuse being 9.14 and base being 13.71/2 = 6.855.
Then, the height = sqrt (9.14^2 - 6.855^2) = sqrt [(9.14+6.855)*(9.14-6.855)] = sqrt(15.995*2.285) = 6.05cm
Therefore, area of the triangle = (1/2)*6.05*13.71 = 41.47 sq. cm.
Thus, area of the triangle is 41.47 sq. cm.
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