Question

a triangle and parallelogram have the same base and the same area if the sides of the triangle are 26 cm 28 cm and 30 cm the parallelogram stands on the base 28 cm find the height of the parallelogram

Answer 1

yes triangle and parallelogram have the same base

Answer 2

Hope u like my process
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Sides of the triangle (a, b, c) =26,28,30 cm.

Semi-Perimeter of triangle (s) = (a+ b+c)/2

$= \frac{26 + 28 + 30}{2} = \frac{84}{2} = 42cm$
Area of the triangle (A) =
$\sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{42(42 - 28)(42 - 26)(42 - 30)} \\ \\ = \sqrt{6 \times 7 \times 14 \times 16 \times 12} \\ \\ = \sqrt{6 \times 7 \times 2 \times 7 \times 4 \times 4 \times 2 \times 6} \\ \\ = 6 \times 2 \times 7 \times 4 = 336 \: \: {cm}^{2}$
Let the height (h) of parallelogram be x cm

Base (b) = 28 cm

Area of parallelogram = h×b = 28x cm²
Given that area of parallelogram and the triangle is equal so,

According to the problem
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$28x = 336 \\ \\ or. \: \: x = \frac{336}{28} = 12 \: cm$
So.

Height of parallelogram is 12 cm.

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