Question

the area of a parallelogram is 338 cm². if it's altitude is twice the corresponding base , determine the base and the altitude.​

Answer 1

Answer :

• Base of parallelogram is 13cm
• Altitude of parallelogram is 26cm

Given that :

• The area of parallelogram is 338 cm²
• If it's altitude is twice the corresponding base

To find :

• Base and altitude of parallelogram

Solution :

To find the base and altitude we must use the formula of area of parallelogram

• Let the base be x

Given that, altitude is twice the corresponding base so,

• Let the height be 2x

We know that

• Area of parallelogram = b × h

Where ,

• b is base
• h is height

Given , Area of parallelogram is 338 cm² so,

➨ Area of parallelogram = base × height

➨ 338 = x × 2x

➨ 338 = 2x²

➨ 2x² = 338

➨ x² = 338/2

➨ x² = 169

➨ x = √169

➨ x = 13 cm

Base of parallelogram is 13 cm

Finding the altitude

➨ 2x

➨ 2(13)

➨ 26cm

Altitude of parallelogram is 26cm

Hence,

• Base of parallelogram is 13 cm
• Altitude of parallelogram is 26cm

Answer 2

$\large \frak \green{ \pmb{ \underline{Given : }}}$

• The area of a parallelogram is 338 cm².
• It's altitude is twice the corresponding base.

$\large \frak \green{ \pmb{ \underline{ To \: find: }}}$

• Find its base and the altitude

$\large \frak \green{ \pmb{ \underline{ Solution: }}}$

$\sf{let \: the \: base \: be \: x.}$

$\sf{ \therefore \: Its \: height \: will \: be \: 2x}$

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

$\sf{ \qquad : \implies \: 338 = x \times 2x}$

$\sf{ \qquad : \implies \: 338 = {2x}^{2} }$

$\sf{ \qquad : \implies \: {x}^{2} = \cancel\frac{338}{2} }$

$\sf{ \qquad : \implies \: {x}^{2} = 169}$

$\sf{ \qquad : \implies \: x = \sqrt{169} }$

$\sf \qquad : \implies{ \underline \pink{ x = 13}}$

______________________________________

$\:$

$\sf{Height = 2x = 2 \times 13 = 26}$

$\sf \color{greenyellow}{ \therefore \: Height \: of \: parallelogram = 26 \: and \: base \: = 13}$

$\qquad \: \: \: \: \: \: \: \tt \color{pink}{ \underline{Hope \: it \: helps \: you \: \ddot \smile}}$