Question

The area of rhombus is 144cm² and one of its diagonals is double the other. The length of the longer diagonal is​

Answer 1

Answer:

AREA OF RHOMBUS =

$\frac{d1 \times d2}{2}$

NOW ONE OF IT'S DIAGONAL IS DOUBLE THE OTHER,

WE GET

ONE DIAGONAL AS=d

other =2d

NOW AREA = 144 CM^2

AREA OF RHOMBUS =

$144 = \frac{d \times 2d}{2} \\ \\ = > 144 \times 2 = 2 {d}^{2} \\ \\ = > 288 = 2 {d}^{2} = > {d}^{2} = \frac{288}{2} = 144 = > d = \sqrt{144} = 12$

WE GET D= 12 cm.

LENTGH OF LONGER DIAGONAL = 2d=2×12=24 cm

Answer 2

$\huge\sf\pink{Answer}$

☞ Diagonals are 12 & 24 cm

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$\huge\sf\blue{Given}$

✭ Area of a Rhombus is 144 cm²

✭ One of its Diagonals is double the other

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$\huge\sf\gray{To \:Find}$

◈ Length of the longer diagonal?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Formula}}$

⪼ $\sf \underline{\underline{Area_{Rhombus} = \dfrac{1}{2} \times d_1\times d_2}}$

$\large\underline{\underline{\sf Let}}$

◕ $\sf D_1 = x$

◕ $\sf D_2 = 2x$

So on substituting these values,

➝ $\sf Area_{Rhombus} = \dfrac{1}{2} \times D_1\times D_2$

➝ $\sf 144 = \dfrac{1}{\cancel{2}} \times x \times \cancel{2}x$

➝ $\sf 144 = 1\times x \times x$

➝ $\sf 144 = x^2$

➝ $\sf \sqrt{144} = x$

➝ $\sf \orange{x = 12}$

So then he length of the diagonals will be,

➳ $\sf D_1 = x = 12 \ cm$

➳ $\sf D_2 = 2x = 12(2) = 24 \ cm$

$\sf\star\: Diagram \: \star$

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