The triangles are similar.
What is the value of x?
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x =
two right triangles. the larger triangle has a long leg of 96 units, short leg of 28 units, and the hypotenuse is labeled 6 x plus 28. the smaller triangle has a long leg of 24 units, short leg of 7 units, and hypotenuse of 25 units.
the sides of the larger triangle are 4 times the sides of the smaller
6x + 28 = 4 * 25
To determine the value of x, we can set up a proportion between the corresponding sides of the two triangles:
(long leg of larger triangle) / (long leg of smaller triangle) = (short leg of larger triangle) / (short leg of smaller triangle)
In this case, the proportion would be:
96 / 24 = 28 / 7
Simplify the proportion:
4 = 4
Since the proportion is true, we can conclude that the value of x can be any number.
To find the value of x, we can use the property of similar triangles. Similar triangles are triangles that have the same shape but different sizes.
In this case, we have two right triangles. Let's label the larger triangle as Triangle A and the smaller triangle as Triangle B.
Triangle A:
Long leg = 96 units
Short leg = 28 units
Hypotenuse = 6x + 28
Triangle B:
Long leg = 24 units
Short leg = 7 units
Hypotenuse = 25 units
For two triangles to be similar, their corresponding sides must be proportional. This means that the ratio of the lengths of their corresponding sides will be equal.
Let's compare the long legs:
Long leg of Triangle A / Long leg of Triangle B = 96 / 24 = 4
Now, let's compare the short legs:
Short leg of Triangle A / Short leg of Triangle B = 28 / 7 = 4
Finally, let's compare the hypotenuses:
Hypotenuse of Triangle A / Hypotenuse of Triangle B = (6x + 28) / 25
Since the triangles are similar, the ratios of their corresponding sides are equal. Therefore, we can set up the following equation:
Long leg ratio = Short leg ratio = Hypotenuse ratio
4 = 4 = (6x + 28) / 25
To find the value of x, we can solve the equation:
4 = (6x + 28) / 25
Cross-multiply to eliminate the fractions:
4 * 25 = 6x + 28
100 = 6x + 28
Subtract 28 from both sides:
100 - 28 = 6x
72 = 6x
Divide by 6 to solve for x:
72 / 6 = x
x = 12
Therefore, the value of x is 12.