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 , find the distance between the longer sides.​

Answer 1

✬ Distance = 9 cm ✬

Step-by-step explanation:

Given:

• Measure of adjacent sides of parallelogram are 36 and 27 cm.
• Distance between the shorter sides is 12 cm.

To Find:

• What is the distance between the longer sides ?

Solution: In parallelogram ABCD we have

• AB = CD = 36 cm
• AD = BC = 27 cm
• AM = 12 cm (distance between AD & BC)

As we know that

★ Area of ||gm = Base × Height ★

Taking base BC

$\implies{\rm }$ Area = BC × AM

$\implies{\rm }$ 27 × 12

$\implies{\rm }$ 324 cm².

Now when base is AB

$\implies{\rm }$ Area = AB × DN

$\implies{\rm }$ Area = 36 × DN

$\implies{\rm }$ 324 = 36 × DN

$\implies{\rm }$ 324/36 = DN

$\implies{\rm }$ 9 cm = DM

Hence, distance between longer sides will be 9 cm.

Answer 2

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 = ?

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

⠀

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

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

⠀

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