Question

Given the pair of triangles are similar find the unknown length of the sides labeled with a variable

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The question is not complete. Let us assume the following:

Let us assume triangle ABC is a right angled triangle with side AB = 24, AC = 32 and the hypotenuse BC = 40.  Triangle PQR is a right angled triangle similar to triangle ABC with side PQ = 27,  PR= b and the hypotenuse QR = a.

Answer:

Two triangles are said to be similar if they have proportional angles or proportional sides that is they have the same shape. For similar triangles, the ratio of their corresponding side are the same.

Given that triangle ABC is similar to triangle PQR, therefore:

$\frac{AB}{AC}=\frac{PQ}{PR}\\ Substituting:\\\frac{24}{32}=\frac{27}{b}\\cross\ multiplying:\\b=\frac{27*32}{24}\\ b=36$

$\frac{AB}{BC}=\frac{PQ}{QR}\\ Substituting:\\\frac{24}{40}=\frac{27}{a}\\cross\ multiplying:\\a=\frac{27*40}{24}\\ a=45$