2210 ARITHMETIC
Hence, the square of either side equals the square of the hypotenuse less the square of the other side.
hyp2 = base2 -j- perp2 hyp = ybase2 + perp2 base2 == hyp2 — perp2 base = yhyp2 —perp2 perp2 = hyp2 — base2 perp = yhyp2 —base2 The base of a right triangle is 24 ft., and the perpendicular is 18 ft. "What is the hypotenuse f
242 = 576 square of base.
182 = 324 square of perpendicular.
900 square of hypotenuse. V900 = 30 length of hypotenuse. Rule. To find the hypotenuse, having the base and perpendicular given: Add the square of the base and the square of the perpendicular, and find the square root of the sum.
Rule. To find the base or perpendicular, having the hypotenuse and other side given: From the square of the hypotenuse subtract the square of the given side, and take the square root of the remainder.
EXERCISE 43.
1. The base of a right triangle is 39 ft., arid the perpendicular is 52 ft. What is the hypotenuse ?
2. What is the diagonal of a rectangle 96 ft. long and 72 ft. wide!
3. A tree was broken 28 ft. from its root, and struck the ground 21 ft. from its base. What was the height of the tree f
4. What must be the length of a ladder to reach to the top of a chimney 48 ft. high, the foot of the ladder being 20 ft. from the chimney?
5. If the top of the ladder mentioned above be lowered 6 feet, how far will the foot stand from the chimney!
6. Two poles are 48 ft. apart. One is 40 ft. high and the other 76 ft. How long a line will connect their tops f
7. Find the diagonal of a square field containing 4 A. 145 sq. rd.
AREA OF SURFACES.
1. To find the area of a rectangle, multiply the base by the altitude.
2. To find the area of a parallelogram, multiply the base by the altitude.
3. To find the area of a triangle, multiply one-half the base by the altitude.
4. To find the area of a trapezoid, multiply one-half the sum of the bases by the altitude.
A polygon is a plane figure bounded by straight lines. A regular polygon is a polygon having all its sides equal. The perimeter of a polygon is the sum of its sides.
