Question

Find the value of t.

Answer 1

Answer:

t =12 m

Step-by-step explanation:

We can use similar triangles and proportions to solve this problem.

Put the smaller triangle on top and the larger triangle on bottom

12         9

------ = -------

16          t

Solve by using cross products

12 t = 9*16

12 t =144

Divide by 12

12t/12 = 144/12

t = 12

Answer 2

$\text{We have similar right triangles (Acute Angle Similarity)}$$\triangle BAC\sim\triangle BED\\\\\dfrac{BA}{AC}=\dfrac{BE}{ED}\\\\\text{We have}\\\\BA=12m,\ AC=9m,\ BE=16m,\ ED=t.\\\\\text{Substitute:}\\\\\dfrac{12}{9}=\dfrac{16}{t}\qquad\text{cross multiply}\\\\12t=(9)(16)\\\\12t=144\qquad\text{divide both sides by 12}\\\\\boxed{\boxed{t=12\ m}}$. Therefore the legs make proportions.