Question

on a photograph of a triangular piece of land, the lengths of the three sides are 5 cm, 8 cm, and 10 cm, respectively. the shortest side of the actual piece of land is 150 m long. find the lengths of the other two sides. the length of the middle - sized side of the triangular piece of land is the length of the largest side of the triangular piece of land is

Explanation:

Step1: Find the scale - factor

The shortest side in the photo is 5 cm and the actual shortest side is 750 m (since 150 m is the longest side and the ratio of sides in the photo is 5:8:10). Let the scale - factor be $k$. We know that if the shortest side in the photo is 5 cm and actual is 750 m (75000 cm), then $k=\frac{75000}{5}=15000$.

Step2: Calculate the middle - sized side

The middle - sized side in the photo is 8 cm. The actual length of the middle - sized side $l_m$ is $l_m = 8\times k$. Substituting $k = 15000$, we get $l_m=8\times15000 = 120000$ cm or 1200 m.

Step3: Calculate the longest side

The longest side in the photo is 10 cm. The actual length of the longest side $l_l$ is $l_l=10\times k$. Substituting $k = 15000$, we get $l_l = 10\times15000=150000$ cm or 1500 m.

Answer:

The length of the middle - sized side of the triangular piece of land is 1200 m and the length of the largest side is 1500 m.