Question

the diagonal of a rectangle is 1 cm more than its length and breadth of the rectangle is 7 cm less than its length.Find the dimensions of rectangle.​

Answer 1

Answer:

length of rectangle = x; breadth = x-7 ; diagonal=x+1.

Step-by-step explanation:

All the angle of a rectangle are 90°.

So by using pythagorus theorem,

Answer 2

Length of rectangle=12 cm

Breadth of rectangle=5 cm

Step-by-step explanation:

Let length of rectangle=x

Breadth of rectangle=x-7

Diagonal of rectangle=x+1

$(x+1)^2=x^2+(x-7)^2$

Using Pythagoras theorem

$(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2$

$x^2+1+2x=x^2+x^2-14x+49$

Using identity:$(a-b)^2=a^2+b^2-2ab$

$(a+b)^2=a^2+b^2+2ab$

$1=2x^2-x^2-14x+49-2x-x^2$

$1-49=x^2-16x$

$-48=x^2-16x$

$x^2-16x+48=0$

$x^2-12x-4x+48=0$

$x(x-12)-4(x-12)=0$

$(x-12)(x-4)=0$

$x-12=0\implies x=12$

$x-4=0\implies x=4$

Length of rectangle=12 cm

Breadth of rectangle=12-7=5 cm

Diagonal of rectangle=12+1=13 cm

If Length of rectangle=4 cm

Breadth of rectangle=4-7=-3 cm

It is not possible because breadth cannot be negative.

#Learn more:

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