Using the Pythagorean Theorem: Using ratios for calculation

Look at the triangle in the figure.

The ratio between AB and BC is 3:4.

Calculate AB and BC.

AB = $3$ BC = $4$

Look at the triangle in the figure.

The ratio between BC and the hypotenuse is 1:4.

AB = $3\sqrt{15}$

What is the length of hypotenuse?

12 cm

Look at the triangles in the diagram.

The ratio between AB and DE is 2:1.

Calculate FE.

$36$ cm

ABC is a right angled isosceles triangle.

What is the ratio of the length of the hypotenuse to the length of the leg?

$\sqrt{2}:1$

Calculate AE given that triangle ABC is isosceles.

$8\frac{1}{3}$

Look at the triangle in the figure.

$a+b=7$

The ratio between CB and AC is 5:3.

Calculate: $a,b$.

$a=3\text{ }b=4$