Question

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.​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\purple{Given:-}}$

• Area of ∆ =Area of parallelogram

• And the sides of ∆

$\sf \bullet 26cm\:\:28cm\:\:30cm$

• First fond the Area of ∆ By heron's formula

$\sf \sqrt{s(s-a)(s-b)(s-c)}\\ \\ \sf\implies s=\dfrac{a+b+c}{2}\\ \\ \sf\implies s=\dfrac{26+28+30}{2}=\cancel{\dfrac{84}{2}}= 42$

$\sf\implies Area=\sqrt{(42(42-26)(42-28)(42-30)}\\ \\ \sf\implies Area=\sqrt{7\times 6\times 16\times 7\times 2\times 6\times 2}\\ \\ \sf\implies Area= 7\times 4\times 6\times 2\\ \\ \sf Area\:of\:\triangle= 336cm{}^{2}$

• Area of ∆ is 336sq.cm

• Now we have to find the height of parallelogram. whose:-

●base is 28cm

●Area =336sq.cm

$\sf{\blue{Area\:of\: \triangle=Area\:of\: parallelogram}}$

$\boxed{\sf{Area\:of\: parallelogram=base\times height}}$

$\sf\implies 336=28\times h\\ \\ \sf\implies \cancel{\dfrac{336}{28}}=h\\ \\ \sf\implies 12=h$

$\underline{\boxed{\purple{\sf{Height\:of\: parallelogram=12cm}}}}$