Question

Two sides of a parallelogram are 14 cm and 8 cm . if the height corresponding to the side of length 14 cm is 7 cm long , find the length of the height corresponding to the side 8 cm .​

Answer 1

Question :-

• Two sides of a parallelogram are 14 cm and 8 cm . if the height corresponding to the side of length 14 cm is 7 cm long , find the length of the height corresponding to the side 8 cm .

$\huge \orange{AηsωeR} ✍$

Given :-

• A parallelogram ABCD in which AB = 14 cm and BC = 8 cm.
• Corresponding height to base AB is DF = 7 cm.

To find :-

• The length of the height (h) corresponding to the side 8 cm .

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

$\boxed{\bf \:Area\:of\:Parallelogram=base\times{height}}$

$\begin{gathered}\Large{\bold{\pink{\underline{CaLcUlAtIoN\::}}}}\end{gathered}$

Case :- 1

⟼ In parallelogram ABCD,

⟼ Base, AB = 14 cm

⟼ Height, DF = 7cm

$\begin{gathered}\bf\red{So,}\end{gathered}$

$\longmapsto\tt\boxed{\bf \:Area\:of\:Parallelogram=b\times{h}}$

$\bf \: ⟼ Area\:of\:Parallelogram = AB \times DF$

$\bf \: ⟼ Area\:of\:Parallelogram = 14 \times 7$

$\bf \: ⟼ Area\:of\:Parallelogram = 98 \: {cm}^{2} ⟼ (1)$

Case :- 2

⟼ In parallelogram ABCD,

⟼ Base, BC = 8cm

$\begin{gathered}\bf\red{Let,} \end{gathered}$

$\begin{gathered}\longmapsto\:\:\bf{Height \:DE \:is \:h\:cm}. \end{gathered}$

$\begin{gathered}\bf\red{So,} \end{gathered}$

$\boxed{\bf \:Area\:of\:Parallelogram=base\times{height}}$

$\bf \: ⟼ Area\:of\:Parallelogram = BC \times DE$

$\bf \: ⟼ Area\:of\:Parallelogram = 8 \times h$

$\bf \: ⟼ Area\:of\:Parallelogram = 8h \: ⟼ (2)$

$\begin{gathered}\bf\pink{Now}\end{gathered}$

On comparing equation (1) and (2), we get

$\bf \: ⟼ 8h = 98$

$\bf \: ⟼ h = \dfrac{98}{8}$

$\bf \: ⟼ h = \dfrac{49}{4} \: cm$

__________________________________________

$\large{\boxed{\boxed{\bf{Explore \ more : - }}}}$

More info:

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = (side)²

Perimeter of square = 4× side

Area of Circle = πr²

Perimeter of Circle = 2πr

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²