Question

The area of the rhombus is 1120 cm2 and the two of its diagonals are in the ratio of 5 : 7 , then find
the length of the longer diagonal.

Answer 1

Given : The Area of the Rhombus is 1120 cm² and two of its diagonals are in the ratio 5:7

To Find : Find the Longer diagonal

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SolutioN : For finding the Diagonals we need to use the formula that is Area = 1/2 × D¹ × D² .Let's Solve :

$\dag$ Calculating the Ratios :

• $\sf{ D_1 }$ = 5y
• $\sf{ D_2 }$ = 7y

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Are{\small_{(Rhombus)}} = \dfrac{1}{2} \times D_1 \times D_2 }}}}}$

Where :

• $\sf{ D_1 }$ = Diagonal 1
• $\sf{ D_2 }$ = Diagonal 2

$\dag$ Calculating the Value of y :

${\longmapsto{\qquad{\sf{ Area = \dfrac{1}{2} \times D_1 \times D_2 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 1120 = \dfrac{1}{2} \times 5y \times 7y }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 1120 \times 2 = 1 \times 5y \times 7y }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 2240 = 1 \times 35y }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 2240 = {35y}^{2} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \dfrac{2240}{35} = {y}^{2} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{2240}{35} = {y}^{2} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 64 = {y}^{2} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \sqrt{64} = y }}}} \\ \\ \\ \ {\qquad \; \; {\longmapsto{\underline{\boxed{\pmb{\frak{ y = 8 }}}}}}} \; {\red{\bigstar}}$

$\dag$ Calculating the Diagonals :

• $\sf{ D_1 }$ = 5y = 5(8) = 40 cm
• $\sf{ D_2 }$ = 7y = 7(8) = 56 cm

$\therefore \; \;$ Longer Diagonal of the Rhombus is 56 cm .

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Answer 2

Answer:

Here is your answer

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