Question

a triangle and a parallelogram stand on same base and are equal in area if the sides of the triangle are 40, 24 and 32 cm and base of the parallelogram is 40 centimetre find the corresponding height of the parallelogram.​

Answer 1

Answer:

Lengths of the sides of the triangle :

• a = 40 cm

• b = 32 cm

• c = 24 cm

Semi - perimeter (s) = (a + b + c)/2

⇒ s = (40 + 32 + 24)/2

⇒ s = 96/2

⇒ s = 48

We know that

Area of the triangle = \begin{gathered}\sf \sqrt{s(s - a)(s - b)(s - c} \\\end{gathered}s(s−a)(s−b)(s−c

\begin{gathered}\sf = \sqrt{48(48 - 40)(48 - 32)(48 - 24)} \\ \\ \sf = \sqrt{48(8)(16)(24)} \\ \\ \sf = \sqrt{384(384)} \\ \\ \sf = \sqrt{ {384}^{2} } \\ \\ \sf = 384 \: cm^{2}\end{gathered}=48(48−40)(48−32)(48−24)=48(8)(16)(24)=384(384)=3842=384cm2

Area of the triangle = 384 cm²

Triangle and parallelogram stand on same base

That means lengths of the corresponding bases are equal

Length of the base of the parallelogram (b) = 40 cm

Let the height of the parallelogram be 'h' cm

Given

Area of the Parallelogram = Area of the triangle

⇒ bh = 384 cm²

⇒ 40h = 384

⇒ h = 384/40

⇒ h = 9.6 cm

Therefore the height of the parallelogram is 9.6 cm

Explanation:

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