Question

area of a square 5 square meter more than 1/2 of the area of a rectangle if the area of the square is 125 meters squared find the dimension of the rectangle if the breadth of the rectangle is 3/5 times of the length of the rectangle​

Answer 1

Answer :-

• The length of the rectangle = 20 m.
• The breadth of the rectangle = 12 m.

To find :-

• The dimensions of the rectangle.

Solution :-

• Let the area of the rectangle be "x" m².

Then 1/2 of the area of the rectangle will be :-

• $\tt \dfrac{1}{2} x$

And 5 square metres more than 1/2 of the rectangle will be :-

• $\tt \dfrac{1}{2} x + 5$

It is given that :-

• The area of the square is 5 square metres more than 1/2 the area of the rectangle.

• The area of the square is 125 m².

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Therefore,

$\hookrightarrow\bf \dfrac{1}{2} x + 5 = 125$

$\hookrightarrow\bf \dfrac{x}{2} + 5 = 125$

$\hookrightarrow\bf \dfrac{x}{2} = 125 - 5$

$\hookrightarrow\bf \dfrac{x}{2} = 120$

$\hookrightarrow\bf x = 120 \times 2$

$\hookrightarrow\bf x = 240 \: m^2$

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• Now, let's find the dimensions of the rectangle as we know it's area!

Let the length of the rectangle be "x" m.

• The breadth of the rectangle is 3/5 times it's length.

Then the breadth of the rectangle will be :-

• $\tt\dfrac{3}{5} x$

We know that :-

$\underline{\boxed{\sf Area \: of \: a \: rectangle = Length \times Breadth}}$

Here,

• Area = 240 m².
• Breadth = "3x/5" m.
• Length = "x" m.

Substituting the given values in this formula,

$\leadsto\rm 240 = x \times \dfrac{3}{5} x$

$\leadsto\rm 240 = x \times \dfrac{3x}{5}$

$\leadsto\rm 240 = \dfrac{3x^2}{5}$

$\leadsto\rm 240 \times 5 = 3x^2$

$\leadsto\rm 1200 = 3x^2$

$\leadsto\rm \dfrac{1200}{3} = x^2$

$\leadsto\rm 400 = x^2$

$\leadsto\rm \sqrt{400} = x$

$\leadsto\rm 20 \: m = x$

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Hence, the dimensions of the rectangle are as follows :-

$\tt Length = x = 20 \: m.$

$\tt Breadth = \dfrac{3}{5}x =\dfrac{3}{5} \times 20 = 12 \: m.$