Question

A rectangle is inscribed in a square creating four isosceles right angles. If the total area of these four triangles is 200. The length of the diagonal of the rectangle is

• A. $10$
• B. $15$
• C. $20$
• D. $25$

Answer 1

The correct option is C $20$

Let the square ABCD is divided into 4 triangles .
$\therefore$ sum of the area of these triangles = area of square ABCD
$\therefore 200=areaofsquareABCD$
$\therefore 200={\left(AB\right)}^2$
$\therefore AB=10\sqrt{2}cm$
$\therefore DiagonalAC=BD=AB\times \sqrt{2}=10\sqrt{2}\times \sqrt{2}=20cm$