The triangles are similar. what is the value of x? enter your answer in the box. 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 given right-angled triangles are similar. The value of x is 12 units.

Given information:

The triangles are similar.

There are two right triangles.

The larger triangle has a long leg of 96 units, a short leg of 28 units, and the hypotenuse is labeled .

The smaller triangle has a long leg of 24 units, a short leg of 7 units, and a hypotenuse of 25 units.

See the attached figure.

It is required to calculate the value of x.

Now, the triangles are similar and hence, their sides will be in the same ratio.

Use the ratio to calculate the value of x,

Therefore, the value of x is 12 units.

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Find the scale factor by dividing the long sides and short side:

96 / 24 = 4

28 / 7 = 4

This means the larger triangle is 4 times bigger than the smaller one.

Now use that scale factor to calculate the hypotenuse:

The length of the smaller hypotenuse is 25, scale that by 4 to get 25 * 4  =100

This means the larger hypotenuse needs to equal 100:

6x+28 = 100

Subtract 28 from each side:

6x = 72

Divide both sides by 6:

x = 72/6

x = 12

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