Question

A parallelogram and rhombus are equal in area. the diagonal of rhombus are 64 cm and 84 cm . If one of the side of the parallelogram is 75 cm . find its height.

Answer 1

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Answer 2

$\huge{\underline{\underline{\mathbb{\red{GIVEN:-}}}}}$

• A parallelogram & a rhombus have equal areas
• Length of one diagonal of rhombus = 64 cm
• Length of another diagonal of rhombus = 84 cm
• One side of parallelogram = 75 cm

$\huge{\underline{\underline{\mathbb{\red{NEED\:TO\:FIND:-}}}}}$

Find the height of the parallelogram = ?

$\huge{\underline{\underline{\mathbb{\red{FORMULA \:USED:-}}}}}$

$\large\bf\blue{b \times h = \frac{1}{2}\times d _{1} \times d _{2}}$

$\huge{\underline{\underline{\mathbb{\red{SOLUTION:-}}}}}$

Let the height of the parallelogram be 'h' cm and base be 'b'

Now, putting the given values in the formula, we get

$\implies$ $\bf{75\times h = \frac{1}{2} \times 64 \times 84}$

$\implies$ $\bf{75\times h = 64\times 42}$

$\implies$ $\bf{h = \frac{64\times42}{75}}$

$\implies$$\bf{h =}$ $\cancel\dfrac{2688}{75}$

$\implies$ $\large\bf{h = 35.84 \:cm}$

$\large{\underline{\underline{\mathbb{\red{FINAL\:ANSWER:-}}}}}$

$\huge{\boxed{\boxed{\bf{\blue{Height = 35.84 \:cm}}}}}$