The value of the other diagonal AC is 36.1 cm.
The top two sides of the sandbox are 29 inches long.
The bottom two sides are 25 inches long.
The diagonal DB has a length of 40 inches.
The figure shows a sandbox in which all the dimensions are given.
Both the diagonals are perpendicular to each other since it is the diagonal of a sandbox. Diagonal DB divides the diagonal AC into two equal parts.
Therefore,
In triangle AOD, apply Pythagoras theorem, since it is a right triangle.
[tex]\begin{aligned}\left(\dfrac{x}{2} \right)^2+y^2&=25^2\\\left(\dfrac{x}{2} \right)^2+y^2&=625\end{aligned}[/tex]
In triangle AOB, apply the Pythagoras theorem, since it is a right triangle.
[tex]\begin{aligned}\left(\dfrac{x}{2} \right)^2+(40-y)^2&=29^2\\\left(\dfrac{x}{2} \right)^2+y^2+1600-80y&=841\\\left(\dfrac{x}{2} \right)^2+625-\left(\dfrac{x}{2} \right)^2+1600-80y&=841\\-80y&=-1384\\y&=17.3\end{aligned}[/tex]
Substitute the value of y in the above expression and solve it for x.
[tex]\begin{aligned}\left(\dfrac{x}{2} \right)^2+(17.3)^2&=625\\\left(\dfrac{x}{2} \right)^2+299.29&=625\\\left(\dfrac{x}{2} \right)^2&=325.71\\\left(\dfrac{x}{2} \right)&=18.05\\x&=36.1\;\rm{cm}\end{aligned}[/tex]
Thus, the value of the other diagonal AC is 36.1 cm.
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