Ratio Problems?

Question

1.The Ratio od the side lengths of an isosceles triangle os 4:4:7, and its perimeter is 52.5 cm. What is the length of the base of the triangle.

2.The Ratio of the angle measures in a parallelogram is 2:3:2:3. What is the measure of each angle.

Answer 1

We know that 4 + 4 + 7 = 15. The sum of the ratios is 15. Then the same relationship a + a + b = 52.5 cm holds. By comparison we get:

52.5 cm / 15 * 4 = two sides which are the same in length

52.5 / 15 * 7 = the long side

The interior angles of the parallelogram must add up to 360 degrees. By this we know that the ratio is 2:3 which added adds up to 360. We know this happens twice so we divide by two.
360 = 2x + 3x = 5x
360 / 5 * 2/2 = one angle
360 / 5 * 3/2 = the other angle