Question

In a rectangle, difference between length and breadth is 7 cm. If length of its diagonal is 13 cm,then find the area of the rectangle.​

Answer 1

Answer:

$60cm^{2}$

Step-by-step explanation:

If the breadth = $x$, length = $x+7$

$13$ is the hypotenus

$13^{2} = (x+7)^{2} + x^{2}\\\\169=x^{2}+14x+49+x^{2}\\\\2x^{2}+14x-120=0\\\\2(x^{2}+7x-60)=0$     $(2\neq 0)$

$x^{2}+7x-60=0\\\\(x-5)(x+12)=0\\\\x=5$   $x=-12$           $(x\geq 0)$

Therefore $x=5$

$5(5+7)=60$

Answer 2

Area of rectangle is 60 cm²

Step-by-step explanation:

Let the length of the rectangle is x and that of width is y.

Then,

x - y = 7 ....(i)

Now, from the attached figure,

Using the Pythagoras theorem,

$x^2+y^2=13^2\\\\x^2+y^2=169$

From equation (i)

$y^2+(7+y)^2=169\\\\y^2+y^2+14y+49=169\\\\2y^2+14y-120=0\\\\(y+12)(y-5)=0\\\\y=-12,5$

Width cannot be negative. Hence, discard y = -12

Thus, y = 5

And hence,

x = 7 + 5

x = 12

Area of the rectangle is given by

A = xy

A = 5× 12

A = 60 cm²

Thus, Area of rectangle is 60 cm²

#Learn More:

The area of a square field is 5184 m square.A rectangular field, whose length equal to the perimeter of the square field. find the area of the rectangular field.

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