A complete and practical solution book for the common school teacher . MENSURATION. 16? (9) .-. The area of the entire polygon AFBDCE= rd. (10) But this is double the area of triangle ABC. .. Area of triangle ABC=875 996785 sq. rd. (11) Equating the two expressions for the area, we have tj»V3= sq. rd. .-. j=44 97874 rd., the side of the triangle —Solved by the author for the Teachers1 Review. PROBLEM 352. A deer is tethered from one corner of an equilateral wall whose sideis 100 ft., by a rope 175 ft. long-: over what area can it graze? Solution. (i) (2) (8). (6)
A complete and practical solution book for the common school teacher . MENSURATION. 16? (9) .-. The area of the entire polygon AFBDCE= rd. (10) But this is double the area of triangle ABC. .. Area of triangle ABC=875 996785 sq. rd. (11) Equating the two expressions for the area, we have tj»V3= sq. rd. .-. j=44 97874 rd., the side of the triangle —Solved by the author for the Teachers1 Review. PROBLEM 352. A deer is tethered from one corner of an equilateral wall whose sideis 100 ft., by a rope 175 ft. long-: over what area can it graze? Solution. (i) (2) (8). (6) (7) FIG. 44. Let AOB be the see that it can graze over |- of (1752X*-)=: sq. over two sectors ATF and BET. (4) We also have a right tri- angle BDT having BD =50 ft., and TB 75 ft., tofind the angle DBT. (5) By triecmomer/, ^DBT =48sVoV. and ZEBT=711841°. and ZIBE+ ZrAF=i43}ia°. From this we have 360° : 148ltt)°::75*X* : ( sq. ft.), the area of the two also grazes over the triangle ABT, whose base is AB^= 100 ft., and altitudeTD or V(52 —502)=25V^ft. (8) This gives (100x25V5)^2=2795 08 sq. ft. (9) Total area grazed over is ++ sq. ft. PROBLEM 353. I have a lot in the form of an equilateral triangle whose sides are100 ft. At each corner stands an orange tree; the height of the firsttree is 10 ft., the second 20 ft., and third 30 ft. At what distance fromthe foot of each tree must a ladder be placed, so that without movingit at the base it may reach the top of each? Find the length of the lad-der. 168
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