Problem A rectangle has an area of $240 \ in^2$ and a diagonal length of $26 \ in$. Find the lengths of its shorter side and longer side. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…

Problem There are two cubes, one large and one small. The sum of their volumes is $2240 \ in^3$ and the difference in the lengths of their sides is $4 \ in$. Find the length of one side of the smaller cube. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$…

Problem There is an isosceles trapezoid with an upper base of $6 \ ft$, a lower base of $12 \ ft$, and a height of $8 \ ft$. Divide this into two isosceles trapezoids of the same area by a line parallel to the bottom base. Then, find the lengths of $EF$ and $GH$. $$…

Problem You decide to buy chestnut, paulownia, and mulberry seedlings for $1,500 \ yen$. The price of a paulownia seedling is $80$ % of that of a chestnut seedling, and the price of a mulberry seedling is half that of a paulownia. Then, how much do the chestnut, paulownia, and mulberry seedlings cost? $$ $$…

Problem As shown in the figure, a large circle and a small circle that circumscribe each other are inscribed in a square. If the area of ​​the square is $235 \ in^2$ and the difference between the diameters of the large and small circles is $2 \ in$, find the diameter of the small circle.…

Problem You want to buy equal amounts of high-grade, medium-grade, and low-grade rice for 5 yen, but for every 1 yen you spend, you get 7 liters of high-grade rice, 8 liters of medium-grade rice, and 10 liters of low-grade rice, respectively. In this case, how many liters of each grade of rice can you…

Problem As shown in the figure, the square $BDEF$ is inscribed in the right triangle $ABC$, and the sum of the areas of $⊿ADE$ and $⊿EFC$ is $150 \ in^2$, and the length of the side $AB$ is $21 \ in$. Find the length of one side of the square $BDEF$. $$ $$ $$ $$…