Question

Two adjacent sides of a parallelogram is 24 and 18cm respectively. If the distance between the longer sides is 12cm, find the distance between shorter sides

Answer 1

Answer :-

Distance between shorter sides is 16 cm.

Solution :-

Lengths of two adjacent sides of a parallelogram = 24 cm and 18 cm

Among lengths of two sides, side measuring 24 cm is a longer side

Finding area through distance between longer sides

Let the longer side be the the base (b) of parallelogram

Distance between longer sider i.e height of the parallelogram (h) = 12 cm

We know that

Area of a parallelogram = bh

= 24 * 12

= 288 cm²

Finding distance beyween shorter sides

Let shorter side measuring 18 cm be the base (b) of the parallelogram

Let the distance between shorter sides i.e height of the parallelogram be 'h' cm

Area of the parallelogram = 288 cm²

⇒ bh = 288

⇒ 18h = 288

⇒ h = 288/18

⇒ h = 16 cm

Therefore the distance between shorter sides is 16 cm.

Answer 2

$\large{\mathfrak{\underline{\underline{Answer :-}}}}$

Given :-

Length of first adjacent side (longer side) = 24 cm

Length of second adjacent side = 12 cm

Distance between the longer sides.

Finding :-

Distance between shorter sides.

Distance between longer sides.

Solution :-

✯ Case 1 :-

Let the longer side be the base of parallelogram (x)

Height of parallelogram = 12 cm

Using Formula :-

$\large{\star{\sf{\boxed{\boxed{Area \: of \: parallelogram \: = \: Base \: {\times}\: Height}}}}}$

⇒ 24 * 12 = Distance between longer sides.

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Distance between Longer sides = 288 cm²

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✯ Case 2 :-

Shorter side measuring = 18 cm

Let the base of parallelogram be b

Area of parallelogram = 288 cm²

Using Formula :-

$\large{\star{\sf{\boxed{\boxed{Area \: of \: parallelogram \: = \: Base \: {\times}\: Height}}}}}$

⟹ Base * Height = 288 cm²

⟹ Base * 18 = 288

⟹ Base = 288/18

⟹ Base = 16 cm

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Area between the shorter side = 16 cm

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