Question

In a parallelogram the base and height are in the ratio of 5:2.if the area of the parallelogram is 360 metersquare,find its base and height

Answer 1

$\huge{\boxed{\mathfrak{Answer:-}}}$

• Let the base and height of parallelogram be x
• then 5x and 2x

• Area of parallelogram=360sq.m

$\boxed{\sf{Area\:of\: parallelogram=Base\times height}}$

$\sf\implies 5x\times 2x=360\\ \\ \sf\implies 10x{}^{2}=360\\ \\ \sf\implies x{}^{2}=\cancel{\dfrac{360}{10}}\\ \\ \sf\implies x{}^{2}=36\\ \\ \sf\implies x=\sqrt{36}\\ \\ \sf\implies x=6m$

$\sf\bullet Height=2\times 6\\ \\ \sf\implies 12m\\ \\ \sf\bullet Base=5\times 6\\ \sf\implies 30m$

$\boxed{\sf{Height=12m}}$

$\boxed{\sf{Base=30m}}$

Answer 2

Solution

• Base and Height Of The Parallelogram are 30m and 12m respectively

Given

• The base and height of the parallelogram are in the ratio 5:2

• Area of the parallelogram = 360 m²

Let x be the common multiple of the ratio

➠ The base and height would be of the form 5x and 2x

$\boxed{\boxed{\sf Area \ Of \ Parallelogram = Height \times Base }}$

$\implies \: \sf \: (5x)(2x) = 360 \\ \\ \implies \: \sf 10x^2 = 360 \\ \\ \implies \ \sf x^2 = 36 \\ \\ \implies \ \boxed{\boxed{\sf x = 6 m}}$

Now,

• Base = 5x = 5(6) = 30 m

• Height = 2x = 2(6) = 12 m