Question

8 cm
a
4 cm
3 cm
figures not drawn to scale.
what is the length of side a in centimeters?
○ 1/6
○ 1/2
○ 2
○ 6

Explanation:

Step1: Identify similar triangles

The two triangles are similar (right - angled, and the ratio of corresponding sides should be equal). Let the length of side \(A\) be \(x\). The ratio of the heights of the two triangles is \(\frac{8}{4}=2\).

Step2: Set up proportion for bases

Since the triangles are similar, the ratio of the bases should be the same as the ratio of the heights. So \(\frac{x}{3}=2\) (because the ratio of heights is 2, so the ratio of bases is also 2).

Step3: Solve for \(x\)

To find \(x\), we multiply both sides of the equation \(\frac{x}{3}=2\) by 3. So \(x = 2\times3=6\).

Answer:

6