Question

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

Answer 1

sending you written solution

Answer 2

Answer:

The length of the carpet is 12 m.

Step-by-step explanation:

Given : A rectangular carpet has an area of 60 sq. m. Its diagonal and longer side together equal 5 times the shorter side.

To find : The length of the carpet is ?

Solution :

Let x and y be the length and width of the rectangle.

The diagonal of the rectangle is  $\sqrt{x^2+y^2}$

Its diagonal and longer side together equal 5 times the shorter side.

According to this statement,

$\sqrt{x^2+y^2}+y=5x$ ......[1]

$\sqrt{x^2+y^2}=5x-y$

Squaring both side,

$x^2+y^2=25x^2+y^2-10xy$

$24x^2=10xy$   .....[2]

Area of the rectangle is $A=xy$

i.e, $xy=60 m^2$

Substitute in the equation [2]

$24x^2=10(60)$

$24x^2=600$

$x^2=25$

$x=\sqrt{25}=5$

Substitute in [2]

$24x^2=10xy$

$24(5)^2=10(5)y$

$24\times 25=50y$

$y=12$

Therefore, The length of the carpet is 12 m.