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3 years ago

Neelam's daily income is ₹ 800. Her daily savings amount is ₹100. What is the ratio of her SAVINGS to her EXPENDITURE?

Mathematics

1 answer:

sveta [45]3 years ago

3 0

Answer: ratio of her SAVINGS to her EXPENDITURE=1:7

Step-by-step explanation:

Neelam's daily income = ₹ 800

Neelam's daily savings amount = ₹100

Therefore her expenditure will be Daily income - Daily savings

= ₹ 800- ₹ 100= ₹ 700

ratio of her SAVINGS to her EXPENDITURE

= 100: 700

=1:7

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Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

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According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

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$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

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This means that you cannot find solutions of this equation. Then CD≠2 cm.

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