perimeter and area of a right triangle?

Question

Find the perimeter and area of a right triangle if the shortest side is 9cm and the longest sideif 15cm. Please explain and workout.


2. What is the circumference and area in feet of circular pool that has a diameter of 20 yards? Work out and explain.

3. Find the volume of a sphere that has a diameter of 9 meters. Work out and explain.

Answer 1

Hi,

You can find the 3rd side using a² + b² = c². It becomes 9² + b² = 15². This solves to b = 12 for the other leg. The perimeter is 9 + 12 + 15 = 36 cm. The area is found by ½bh or ½(9)(12) = 54 cm².

The perimeter is 36 cm and the area is 54 cm².

The circumference is found by C = πd. The circumference is 20π or 62.83 cm. The area of a circle is found by A = πr² and this area is 100π or 314.159 cm²

The volume of the sphere is V = 4/3πr³ which is 4/3π(4.5)³ which equals 121.5π cm³ or 381.70 cm³.

I hope that helps!! :-)

Answer 2

1. It's a 3/4/5 triangle, so the other side is 12 cm long.
(pythagorean theorum: a^2 + b^2 = c^2).

That means the perimeter is 12 + 9 + 15 cm, or 36 cm.

area = 1/2 base * height, or 1/2 9 * 12, or 54 cm.

2. Hint - circumference of a circle = diameter * pi. (3.141)

3. Hint - volume of a sphere = 4/3 * pi * radius^3

Answer 3

1) You know the hypotenuse is 15 and one of the legs is 9, so use Pythagoras to find the length of the other leg. Use this to find the perimeter (summing all the sides) and the area ( (1/2)bh, which comes down to half of one leg times the length of the other leg).

2) Use the formulas C = π D, and A = π r^2, where D is the diameter and r = D/2, the radius.

3) Use the fomula for the volume of a sphere, (4/3)π r^3. Again, use the fact that the radius is half of the diameter.

Answer 4

1
In right triangle longest side = hypotenuse = 15 cm
so (third side)^2 = 15^2 - 9^2 = 225 - 81 = 144
third side =sqrt(144) = 12 cm
perimeter = sum of all sids = 9 + 12 + 15 = 36 cm
Area = (bh)/2 = (9)(12)/2 = 54 square cm
2.
pool dia = 20 yards
radius = 20/2 = 10 yards
circumference = (2)(Pi)r = 2(22/7)(10)= 440/7 = 62.86 yards
area = (pi)(r^2) = (22/7)(10^2) = (22)(100)/7 = 2200/7
= 314.3 sq.yards
3
diameter of sphere = 9 meters
radius = 9/2 meters
volume of sphere = (4/3)(pi)(r^3) = (4/3)(22/7)(9/2)^3
= (4/3)(22/7)(729/8)
= 381.86 cubic meters

Answer 5

1.Perimeter and area of a right angled triangle having sides a < b < c are
P = a + b + c and A = ab/2
Given a = 9cm and c = 15cm we get
b = 12cm from a^2 + b^2 = c^2
P = 9cm + 12cm + 15cm = 36cm.
A = 9cmx12cm/2 = 54sqcm.
2. Diameter d = 2r = 20yds = 60ft, r = 30ft
Circumference C = 2pir
= 2(3.142)(30ft)
= 188.52ft
Area A = pir^2
=3.142(30ft)^2
=2827.8sqft
3. Diameter d = 2r = 9m => r = 4.5m
Volume V =(4/3)pir^3
=(4/3)(3.142)(4.5m)^3
=381.753cum

Answer 6

perimeter =6+5+5=16 cm. area= (base*height)/2 =6*4/2 =12 cm^2

Answer 7

This is a 9,12,15 right triangle
So perimeter is is 36 cm and area is 9*12/2 = 54 cm^2

Circumference = pi*d = 20*pi yards
Area = pir^2 = 100pi

V= 4/3 pir^3 = 4/3*pi*81/8 = 40.5*pi m^3

Answer 8

do your own homework.