Question 1150827
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the diagonal of a rectangle is 15cm, and the perimeter is 38cm. what is the area?
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<pre>
Let "a" and "b" be the lengths of two adjacent sides of the rectangle.


Then  

    a + b = 19  =  {{{38/2}}}      (1) 

    {{{a^2}}} + {{{b^2}}} = {{{15^2}}} = 225   (2)


Square both sides of the equation (1);  keep equation (2) as is.


    {{{a^2 + 2ab + b^2}}} = {{{19^2}}} = 361   (1')

    {{{a^2}}}  +  {{{b^2}}} = 225         (2')


Subtract equation (2')  from equation (1')

     2ab = 361 - 225 = 136.


Now,  2ab  is two times the area of the rectangle;  hence, the area of the rectangle is  {{{136/2}}} = 68 square centimeters.


<U>ANSWER</U>.  The area of the rectangle is 68 square centimeters.
</pre>

Solved.


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The lesson to learn:


<pre>
    In order to solve this problem, you do not need solve quadratic equation.
</pre>