A rectangular carpet has an area of $60 m^{2}$ . Its diagonal and longer side together equal $5$ times the shorter side. The length of the carpet is

5 m

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12 m

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13 m

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14.5 m

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Solution

The correct option is A $12 m$
We have, $l e n g t h \times b r e a d t h = 60 m^{2}$

And, $\sqrt{l^{2} + b^{2}} + l = 5 b$

Now, $l^{2} + b^{2} = (5 b - l)^{2}$

Or, $24 b^{2} - 10 l b = 0$

Or, $24 b^{2} - 600 = 0$

Or, $b^{2} = 25$

Hence, $b = 5$

Hence, $l = (\frac{60}{5}) m = 12 m$

So, length of the carpet $= 12 m$ .

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A rectangular carpet has an area of 60 m2. Its diagonal and longer side together equal 5 times the shorter side. The length of the carpet is

The correct option is A 12 mWe have, length×breadth=60m2 And, √l2+b2+l=5b Now, l2+b2=(5b−l)2 Or, 24b2−10lb=0 Or, 24b2−600=0 Or, b2=25 Hence, b=5 Hence, l=(605)m=12m So, length of the carpet =12m.

A rectangular carpet has an area of $60 m^{2}$ . Its diagonal and longer side together equal $5$ times the shorter side. The length of the carpet is