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

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 is10152025

Toppr Admin · Accepted Answer

Let the square ABCD is divided into 4 triangles .
$∴$ sum of the area of these triangles = area of square ABCD
$∴ 200 = a r e a o f s q u a r e A B C D$
$∴ 200 = {(A B)}^{2}$
$∴ A B = 10 \sqrt{2} c m$
$∴ D i a g o n a l A C = B D = A B \times \sqrt{2} = 10 \sqrt{2} \times \sqrt{2} = 20 c m$

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 is10152025

Let the square ABCD is divided into 4 triangles .∴ sum of the area of these triangles = area of square ABCD∴200=areaofsquareABCD∴200=(AB)2∴AB=10√2cm∴DiagonalAC=BD=AB×√2=10√2×√2=20cm

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

$10$
$15$
$20$
$25$