Question

The adjacent sides of a parallelogram are 36cm and 27cm if the distance between the shorter sides is 12 cm, find the distance between the longer side.

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Answer 1

Answer:

The distance between the longer side is 9cm.

Step-by-step explanation:

Given that, AB and DC = 36cm

And AD and BC = 27cm

Also, given that that the distance between the shorter sides is 12 cm.

Let's first find out the area of the given parallelogram:

Area of parallelogram = b × h

Breadth is known to us as 27cm and height here is 12cm.

Area of the parallelogram ABCD = 27cm × 12cm

Area of the parallelogram ABCD = 324cm²

The question has asked us to find the length of AE. Let's form an equation as follows;

$\sf \implies AE \times DC = 324cm^2$

$\sf \implies AE \times 36cm = 324cm^2$

$\sf \implies AE = \dfrac{324cm^2}{36cm}$

AE = 9cm

So, the distance between the longer side is 9cm.

Answer 2

${\bold{\sf{\underline{Understanding \: the \: concept}}}}$

✠ This question says that there is a paralloelogram of adjacent sides 36 cm and 27 cm. Afterwards this question says that we have to find the distance between the shorter side and it is 12 cm now we have to find the distance between longest side.

${\bold{\sf{\underline{Assumptions}}}}$

✠ Let point AB and HI as 36 cm

✠ Let point AH and BI as 27 cm

${\bold{\sf{\underline{Given \: that}}}}$

✠ AB and HI measure 36 cm

✠ AH and BI measure 27 cm

✠ Distance between shorter side =12 cm

${\bold{\sf{\underline{To \: find}}}}$

✠ Distance between longest side

${\bold{\sf{\underline{Solution}}}}$

✠ Distance between longest side = 09 cm

${\bold{\sf{\underline{Using \: concepts}}}}$

✠ Area of paralloelogram formula.

${\bold{\sf{\underline{Using \: formulas}}}}$

✠ Area of paralloelogram = B × H

${\bold{\sf{\underline{These \: also \: means}}}}$

✠ B means Base

✠ H means Height

✠ A means Area

${\bold{\sf{\underline{Full \: solution}}}}$

↦ Area of parallelogram = B × H

↦ Area of parallelogram = 27 × 12

↦ Area of parallelogram = 324 cm²

Now let's find the height of point AE hence,

↦ AE × HI = 324 cm²

↦ AE × 36 = 324 cm²

↦ AE = 324 / 36

↦ AE = 162 / 18

↦ AE = 81 / 9

↦ AE = 9 cm

Henceforth, the distance between the longer side = 9 cm.

Note : Hloh..! Please see the diagram also. It help you to understand the concept easily. Thank you.