the ratio of the side lengths of a triangle is 4:7:5 and its perimeter is 64 cm. What is the length of the shortest side?
Ratios are usually good to set up like this:
4x+7x+5x=64 in this case. 4x = the shortest side, 7x = the longest side, and 5x = the middle side. Then solve for x.
16x+64
x=4
Then plug 4 back in for x to see what the individual side lengths are.
4*4=16 for the shortest side.
The ratio of the lengths of a triangle is 3 :4 :5. If the shortest side of a triangle is 24 cm, find the total of the length of other two sides of this triangle.
To find the length of the shortest side of the triangle, we need to determine the actual side lengths using the given ratio and the perimeter of the triangle.
Step 1: Add the ratio values
The ratio of the side lengths is 4:7:5, so the total number of parts is 4 + 7 + 5 = 16.
Step 2: Calculate the length per part
Divide the perimeter of the triangle by the total number of parts to get the length per part.
Length per part = Perimeter / Total number of parts = 64 cm / 16 = 4 cm.
Step 3: Multiply the length per part by the corresponding ratio value
Multiply the length per part by 4, since it corresponds to the shortest side in the ratio.
Length of the shortest side = Length per part * Ratio value = 4 cm * 4 = 16 cm.
Therefore, the length of the shortest side of the triangle is 16 cm.
To find the length of the shortest side of the triangle, we need to determine the actual lengths of the sides represented by the given ratio.
Step 1: Let's assign variables to represent the side lengths. Let's call the side lengths 4x, 7x, and 5x, where x is a positive constant.
Step 2: According to the problem, the perimeter of the triangle is 64 cm. The perimeter is the sum of all three side lengths, so we can set up an equation to solve for x:
4x + 7x + 5x = 64
Step 3: Combine like terms:
16x = 64
Step 4: Solve for x by dividing both sides of the equation by 16:
x = 64 / 16
x = 4
Step 5: Now that we have the value of x, we can find the length of the shortest side:
Shortest side = 4x = 4 * 4 = 16 cm.
Therefore, the length of the shortest side of the triangle is 16 cm.