1. **Problem statement:** We have a truss structure with base segments $a=3000$, $b=2500$, and a vertical segment $c=2300$. We need to find the lengths of the four bars $d$, $e$, $f$, and $g$. 2. **Understanding the structure:** The base is composed of two horizontal segments $a$ and $b$ joined at a point. Above this junction, there is a vertical segment $g$ down to the base. From the left bottom to the top right, there is a long slanted bar with a kink at the junction of $a$ and $b$. From this kink, a lower slanted bar $f$ goes down to the bottom of the right vertical segment $c$. Another bar $e$ goes vertically down from the kink to the base at the $a/b$ junction. 3. **Assign coordinates:** - Let the left bottom point be at $(0,0)$. - The junction between $a$ and $b$ is at $(a,0) = (3000,0)$. - The right bottom point is at $(a+b,0) = (5500,0)$. - The top right vertical segment $c$ goes from $(a+b,0)$ up to $(a+b,c) = (5500,2300)$. 4. **Coordinates of the kink point:** - The kink is vertically above the junction of $a$ and $b$, so at $(3000,y)$. - The vertical bar $g$ connects this kink point down to the base at $(3000,0)$. - The top right point is at $(5500,2300)$. 5. **Calculate length $g$:** - Since $g$ is vertical from $(3000,y)$ to $(3000,0)$, its length is $g = y$. 6. **Calculate length $d$:** - $d$ is the long upper slanted bar from left bottom $(0,0)$ to the kink $(3000,y)$. - Length $d = \sqrt{(3000-0)^2 + (y-0)^2} = \sqrt{3000^2 + y^2}$. 7. **Calculate length $e$:** - $e$ is vertical from kink $(3000,y)$ down to base $(3000,0)$. - So $e = y$ (same as $g$). 8. **Calculate length $f$:** - $f$ is the lower slanted bar from kink $(3000,y)$ to bottom of right vertical segment $(5500,0)$. - Length $f = \sqrt{(5500-3000)^2 + (0 - y)^2} = \sqrt{2500^2 + y^2}$. 9. **Calculate length $c$:** - Given as $2300$ (vertical segment at right). 10. **Find $y$ using the geometry:** - The top right point is at $(5500,2300)$. - The long upper slanted bar $d$ goes from $(0,0)$ to $(3000,y)$, then from kink to top right point. - The upper slanted line is composed of two segments: $d$ and the segment from kink to top right. 11. **Calculate the length of the segment from kink to top right:** - This segment length is $h = \sqrt{(5500-3000)^2 + (2300 - y)^2} = \sqrt{2500^2 + (2300 - y)^2}$. 12. **Since the upper slanted line is continuous, the total length is $d + h$. But we don't have total length, so we use the vertical segment $g$ and $e$ equal to $y$ and the vertical segment $c=2300$ to find $y$ by considering the right triangle formed by $f$, $b$, and $y$. 13. **Use the right triangle with base $b=2500$, height $y$, and hypotenuse $f$:** $$ f = \sqrt{b^2 + y^2} = \sqrt{2500^2 + y^2} $$ 14. **Use the right triangle with base $a=3000$, height $y$, and hypotenuse $d$:** $$ d = \sqrt{a^2 + y^2} = \sqrt{3000^2 + y^2} $$ 15. **Use the right triangle with base $b=2500$, height $(2300 - y)$, and hypotenuse from kink to top right $h$:** $$ h = \sqrt{2500^2 + (2300 - y)^2} $$ 16. **Since the top right vertical segment $c=2300$ is fixed, and the kink is vertically above the $a/b$ junction, the vertical distance $y$ must satisfy the geometry. We can find $y$ by considering the vertical segment $g = y$ and the vertical segment $c=2300$. 17. **Assuming the kink lies on the line connecting left bottom $(0,0)$ and top right $(5500,2300)$, find $y$ at $x=3000$:** - The slope of the line is $m = \frac{2300 - 0}{5500 - 0} = \frac{2300}{5500} = \frac{23}{55}$. - The line equation is $y = m x = \frac{23}{55} x$. - At $x=3000$, $$ y = \frac{23}{55} \times 3000 = \frac{23 \times 3000}{55} = \frac{69000}{55} = 1254.545... $$ 18. **Calculate lengths now:** - $g = y = 1254.545$ - $d = \sqrt{3000^2 + 1254.545^2} = \sqrt{9,000,000 + 1,573,553} = \sqrt{10,573,553} \approx 3250.93$ - $e = y = 1254.545$ - $f = \sqrt{2500^2 + 1254.545^2} = \sqrt{6,250,000 + 1,573,553} = \sqrt{7,823,553} \approx 2797.42$ **Final answers:** $$ d \approx 3250.93 $$ $$ e \approx 1254.55 $$ $$ f \approx 2797.42 $$ $$ g \approx 1254.55 $$