Question

the length of the rectangle is 1 cm more than its breadth. the diagonal is 29 cm. find the area of the rectangle. ​

Answer 1

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Answer 2

The area of the rectangle is 420 cm².

Step-by-step explanation:

Given : The length of the rectangle is 1 cm more than its breadth. The diagonal is 29 cm.

To find : The area of the rectangle ?

Solution :

Let the breadth of the rectangle be b=x.

The length of the rectangle is 1 cm more than its breadth.

Length is l=x+1

The diagonal of the rectangle is

$d^2=l^2+b^2$

Substitute the values,

$(29)^2=(x+1)^2+x^2$

$841=x^2+1+2x+x^2$

$2x^2+2x-840=0$

$x^2+x-420=0$

$x^2+21x-20x-420=0$

$x(x+21)-20(x+21)=0$

$(x+21)(x-20)=0$

$x=-21,20$

Reject x=-21.

The value of x is 20.

The breadth of the rectangle is 20.

The length of the rectangle is l=20+1=21

The area of the rectangle is $A=l\times b$

$A=20\times 21$

$A=420\ cm^2$

Therefore, the area of the rectangle is 420 cm².

#Learn more

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