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A rectangle is 2cm longer than it’s width. If the diagonal of the rectangle is 10cm determine the dimensions of the rectangle

Sagot :

Let x be the width of the rectangle. Then x+2 is the length of the rectangle.

Given diagonal is of 10 cm.

By Pythagorean theorem,

[tex]\begin{gathered} x^2+(x+2)^2=10^2 \\ x^2+x^2+4x+4=100 \\ 2x^2+4x+4=100 \\ x^2+2x+2=50 \\ x^2+2x-48=0 \end{gathered}[/tex]

Factorize the quadratic equation.

[tex](x+8)(x-6)=0[/tex]

implies x = -8 and x = 6.

Since dimension can't be negative, the value of x is 6.

Thus, the length of the rectangle is 8 and width of the rectangle is 6.

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