Question

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

Answer 1

Your answer is $\bold\boxed{9\:cm}$

Here is how :-

Given, the distance between shorter sides i.e 27 is 12 cm. Let the distance between larger side be h cm.
(Distance between two sides is actually it's corresponding altitude)


If we assume 27cm as base, then height will be 12cm

We know that, area of a parallelogram = base × height.

Hence area = 27 × 12 = 324cm²


We also know that if we assume 36 cm as base and h cm as height then we will get

Area will remain the same because it's the same parallelogram.

Hence, 36 × h = 324

=> h = 324/36

h = 9cm

Hence the distance between larger side is
$\boxed{9cm}$

Hope it helps dear friend ☺️✌️

Answer 2

Step-by-step explanation:

Answer:

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(8.6,3){\large\tt{A}}\put(7.7,0.9){\large\tt{B}}\put(9.5,0.7){\sf{\large{36 cm}}}\put(11.1,0.9){\large\tt{C}}\put(8,1){\line(1,0){3}}\qbezier(11,1)(11.5,2)(12,3)\put(9,3){\line(3,0){3}}\put(9.1,2){\sf{\large{12 cm}}}\put(9,1){\line(0,1){2}}\qbezier(8,1)(8.5,2)(9,3)\qbezier(11.5,2)(11.5,2)(9,3)\put(12.1,3){\large\tt{D}}\put(11.5,1.6){\sf{\large{27 cm}}}\put(11.65,2){\large\tt{M}}\put(8.9,0.7){\large\tt{N}}\end{picture}$

Adjacent Sides of Parallelogram are 36 cm and 27 cm

Distance between Shorter Sides = 12 cm

Distance between Longer Sides = ?

$\bigstar\:\boxed{\sf Area\:of\:Paralleogram=Base \times Height}$

⠀

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Area\:of\:\parallel\: _{with \:base\:BC}=Area\:of\:\parallel\:_{with \:base\:CD}\\\\\\:\implies\sf Base \times Height = Base \times Height\\\\\\:\implies\sf BC \times AN=CD \times AM\\\\\\:\implies\sf 36 \times 12 =27 \times AM\\\\\\:\implies\sf \dfrac{36 \times 12}{27} = AM\\\\\\:\implies\sf 4 \times 4 = AM\\\\\\:\implies\underline{\boxed{\sf AM = 16\:cm}}$

⠀

$\therefore\:\underline{\textsf{Distance between longer sides is \textbf{16 cm}}}.$