Question

Mary makes a quilting pattern with two similar isosceles triangles. In one triangle, the base is 1.4 in. and the other side lengths are 3.2 in. Find the side lengths, r, of the other triangle if its base is 4.48 in.

Answer 1

Answer:

10.24 in

Explanation:

In similar triangles, the proportion of the corresponding sides is constant. So, we can write the following equation:

$\frac{Base}{Side\text{ Lengths}}=\frac{1.4\text{ in}}{3.2\text{ in}}=\frac{4.48\text{ in}}{r}$

Where r is the side length of the other triangle.

So, solving for r, we get:

$\begin{gathered} \frac{1.4}{3.2}=\frac{4.48}{r} \\ 1.4r=3.2(4.48)_{} \\ 1.4r=14.336 \\ \frac{1.4r}{1.4}=\frac{14.336}{1.4} \\ r=10.24 \end{gathered}$

Therefore, the side lengths of the other triangle are 10.24 in.