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(C) For the given triangle,the sides are $a = 28 \, cm$,$b = 30 \, cm$,and $c = 26 \, cm$.The semi-perimeter $s$ is calculated as:$s = \frac{a + b + c

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(C) For the given triangle,the sides are $a = 28 \, cm$,$b = 30 \, cm$,and $c = 26 \, cm$.The semi-perimeter $s$ is calculated as:$s = \frac{a + b + c}{2} = \frac{28 + 30 + 26}{2} \, cm = \frac{84}{2} = 42 \, cm$.Using Heron's formula,the area of the triangle is:$	ext{Area} = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{42(42 - 28)(42 - 30)(42 - 26)} \, cm^2$$= \sqrt{42 	imes 14 	imes 12 	imes 16} \, cm^2$$= \sqrt{(6 	imes 7) 	imes (2 	imes 7) 	imes (6 	imes 2) 	imes 16} \, cm^2$$= \sqrt{6^2 	imes 7^2 	imes 2^2 	imes 4^2} \, cm^2 = 6 	imes 7 	imes 2 	imes 4 \, cm^2 = 336 \, cm^2$.Since the area of the parallelogram is equal to the area of the triangle:$	ext{Area of the parallelogram} = 336 \, cm^2$.The formula for the area of a parallelogram is $	ext{base} 	imes 	ext{height}$.$28 \, cm 	imes h = 336 \, cm^2$$h = \frac{336}{28} \, cm = 12 \, cm$.Thus,the height of the parallelogram is $12 \, cm$.

$A$ triangle and a parallelogram have the same base and the same area. If the sides of the triangle are $26 \, cm$,$28 \, cm$,and $30 \, cm$,and the parallelogram stands on the base $28 \, cm$,find the height of the parallelogram. (in $, cm$)

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