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(99 POINTS) Using similarity solve for x. Show all work

(99 POINTS) Using similarity solve for x. Show all work-example-1

2 Answers

3 votes

Shorter Length/Hypotenuse = ab/ac = ad/ab

x/9+16 = 9/x

x^2 = 9 x (9 + 16)

= 9 x 25

= 225

square root of 225 = 15

x = 15

User Huon
by
8.6k points
4 votes

General Idea:

In any right triangle,

1. The altitude to the hypotenuse is the geometric mean between the segments into which is separates the hypotenuse.

2. Each leg is a geometric mean of the hypotenuse and the segment of the hypotenuse adjacent of the leg.

Applying the concept:

Step 1: We need to label the given diagram and set up a proportion by comparing the similar triangles as provided in attached figure.

Setting up the proportion, we get...


(Shorter \; Leg)/(Hypotenuse)=(AB)/(AC)=(AD)/(AB)\\\\(x)/(9+16)=(9)/(x)\\Cross \; Multiplying \; we \; get...\\\\x^2=9(9+16)\\x^2=9(25)\\x^2=225\\Take \; square \; root \; on \; both \; sides\\\\√(x^2)=√(225)\\x=15

Conclusion:


x=15 \; cm


(99 POINTS) Using similarity solve for x. Show all work-example-1
User Ana GH
by
7.8k points

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