A Triangle has sides 4,8,and 11. In a similar triangle the shortest side is 8 and the longest side is x.
a) Write a proportion that models the situation.
b) Solve the proportion for x.
8 : y : x = 4 : 8 : 11 , where y is the middle and x is the longest
for x:
8/4 = x/11
4x = 88
x = 22
a) The proportion that models the situation is:
\( \frac{4}{8} = \frac{11}{x} \)
b) To solve the proportion for x, we can cross-multiply and then solve for x:
\( 4x = 8 \cdot 11 \)
\( 4x = 88 \)
\( x = \frac{88}{4} \)
\( x = 22 \)
Therefore, the value of x is 22.
a) To write a proportion that models the situation, we can compare the lengths of the corresponding sides in the two triangles. Let's compare the shortest sides of the two triangles: 4 and 8, and compare the longest sides: 11 and x.
The proportion can be written as:
(4/8) = (11/x)
b) To solve the proportion for x, we can cross-multiply and then solve for x.
Cross-multiplying the proportion, we have:
4*x = 8*11
Simplifying this expression:
4x = 88
To solve for x, we need to isolate it on one side of the equation. We can divide both sides by 4:
(4x)/4 = 88/4
x = 22
Therefore, the value of x is 22.