A right triangle has leg lengths of 7 and 24 units. A second triangle is similar to the first triangle and has a hypotenuse of 100 units. What is the length, in units, of the shorter leg of the second triangle?

ProffesorNobody Jun 9, 2019

#1**+2 **

By the pathogorean theorum, the hypotonuse of the first triangle is \(\sqrt{7^2+24^2} = 25\)

Because the two triangles are similar, the rario between the side lengths will be the same on both triangles.

\(\frac{100}{short leg}=\frac{25}{7}\)

cross multiply

700=25*short leg

divide by 25

short leg of the second triangle=\(\boxed{28}\)

.power27 Jun 10, 2019

#2**+2 **

ratio of your first triangle is 7-24-25 (it's a pythagorean triple, you could also find 25 using pythagoreon thereom)

ratio of bigger tirangle is x:x:100. To get from 25 to 100, x4. 7 x 4 = 28, 24 x 4 = 96

The ratio of your bigger triangle is 28 : 96 : 100

The shorter leg value of the second triangle is 28

Drazil Jun 10, 2019