<p>A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths <img alt="$15$" height="13" src="https://latex.artofproblemsolving.com/f/1/9/f1965fae079a9ba2c0726c307070c2355dfcb213.png" width="17" /> and <img alt="$25$" height="12" src="https://latex.artofproblemsolving.com/6/6/6/66644fd9f411299c3c1eabf151b5f601c9ef6c21.png" width="17" /> meters. What fraction of the yard is occupied by the flower beds?</p> <center><img alt="[asy] unitsize(2mm); defaultpen(linewidth(.8pt)); fill((0,0)--(0,5)--(5,5)--cycle,gray); fill((25,0)--(25,5)--(20,5)--cycle,gray); draw((0,0)--(0,5)--(25,5)--(25,0)--cycle); draw((0,0)--(5,5)); draw((20,5)--(25,0)); [/asy]" height="52" src="https://latex.artofproblemsolving.com/3/e/e/3ee29f78e4a8eecdb8faec4092f2f1c361a869e4.png" width="238" /></center>

Question No: 276

A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths $15$ and $25$ meters. What fraction of the yard is occupied by the flower beds?

$[asy] unitsize(2mm); defaultpen(linewidth(.8pt)); fill((0,0)--(0,5)--(5,5)--cycle,gray); fill((25,0)--(25,5)--(20,5)--cycle,gray); draw((0,0)--(0,5)--(25,5)--(25,0)--cycle); draw((0,0)--(5,5)); draw((20,5)--(25,0)); [/asy]$

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