Question

The base of a parallelogram is 9cm and altitude is 4.3cm. If the other altitude is 4.5cm, find the perimeter of the parallelogram?

Answer 1

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↠ The base of a parallelogram is 9cm and altitude is 4.3cm. If the other altitude is 4.5cm, find the perimeter of the parallelogram?

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$\underline{\boxed{\bold{Important\;Information}}}$  

❏ Opposite sides of parallelogram are equal.

❏ Opposite angles of parallelogram are equal.

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$\underline{\boxed{\bold{Given}}}$

❏ First altitude = 4.3 cm

❏ First base = 9 cm

❏ Second altitude = 4.5 cm

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Let's Start !

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✧ Here we are given measure of one base of parallelogram. So side opposite to this base is also equal in measure. So now we need to find other base in order to find perimeter.

⭐ Since Area of closed polygon doesn't changes if we measure from different sides. In short we have to equate both the areas by both altitudes and bases.

Mathematically ,

$\bold { \red {Area = A_1 = (Base)_1 \; \times \; (Altitude)_1} }$

$\bold { \blue {Area = A_2 = (Base)_2 \; \times \; (Altitude)_2} }$

$\boxed { \bold { \green { A_1 = A_2} } }$

$\bold {:\implies (Base)_1 \; \times \; (Altitude)_1 = (Base)_2 \; \times \; (Altitude)_2 }$

$\bold {:\implies 9 \; \times \; 4.3 = (Base)_2 \; \times \; 4.5 }$

$\boxed { \bold { \pink {:\implies (Base)_2 = 8.6 \; cm } } }$

∴ Perimeter = 2 × (Base₁ + Base₂)

                    = 2 × (9 + 8.6) cm

                     = 2 × (17.6) cm

                     = 35.2 cm

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$\boxed{\boxed{\bold{\therefore Perimeter \; of \; parallelogram = 35.2 }}}$

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Hope this helps u.../

【Brainly Advisor】

Answer 2

$\underline{\boxed{\bold{\blue{Question}}}}$

• The base of a parallelogram is 9cm and altitude is 4.3cm. If the other altitude is 4.5cm, find the perimeter of the parallelogram?

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$\underline{\boxed{\bold{\blue{More\;Information}}}}$

  

• Opposite sides of parallelogram are equal.

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$\underline{\boxed{\bold{\blue{Given}}}}$

• First altitude = 4.3 cm

• First base = 9 cm

• Second altitude = 4.5 cm

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$\underline{\boxed{\bold{\blue{Answer}}}}$

• ➪Here we are given measure of one base of parallelogram.

• ➪So side opposite to this base is also equal in measure.

• ➪So now we need to find other base in order to find perimeter.

• ➪Since Area of closed polygon doesn't changes if we measure from different sides.

• ➪In short we have to equate both the areas by both altitudes and bases.

Mathematically ,

$\bold { \red {Area = A_1 = (Base)_1 \; \times \; (Altitude)_1} }$

$\bold { \blue {Area = A_2 = (Base)_2 \; \times \; (Altitude)_2} }$

$\boxed { \bold { \blue { A_1 = A_2} } }$

$\bold {:\implies (Base)_1 \; \times \; (Altitude)_1 = (Base)_2 \; \times \; (Altitude)_2 }$

$\bold {:\implies 9 \; \times \; 4.3 = (Base)_2 \; \times \; 4.5 }$

$\boxed { \bold { \blue {:\implies (Base)_2 = 8.6 \; cm } } }$

∴ Perimeter = 2 × (Base₁ + Base₂)

                    = 2 × (9 + 8.6) cm

                     = 2 × (17.6) cm

                     = 35.2 cm

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$\boxed{ \fcolorbox{blue}{black}{ \boxed{\bold{ \blue{\therefore Perimeter \; of \; parallelogram = 35.2}}}}}$

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