# A triangle and a parallelogram have the same base and the same area at the side of the triangle are 126cm 120cm and 130cm and parallelogram stand on the base 120 cm find the corresponding reight of the parallelogram

Side of triangle 126cm, 120cm, and 130cm

its semi-perimeter,

$s = \frac{a+b+c}{2}$

Now,

$s = \frac{126+120+130}{2}= \frac{376}{2} = 188 cm$

We use Heron's formula,  Area of triangle

$= \sqrt {s(s-a)(s-b)(s-c)}$

Put the value, Area of triangle

$= \sqrt {188(188-126)(188-120)(188-130)} \\ = \sqrt {188\times 62 \times 68 \times 58} \\ = 6780.21cm^{2}$

Since a parallelogram and a triangle have the same base and same area, now

Area of parallelogram = Area of trianble

$120 \times height(h) = 6780.21 \\ h = 56.50 cm$

Hence, corresponding height of parallelogram with base 120cm = 56.50 cm

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