Question

In ∆ABC with m∠C = 90° the sides satisfy the ratio BC:AC:AB = 4:3:5. If the side with middle length is 12 cm, find: 1) The perimeter of ∆ABC; 2) The area of ∆ABC; 3) The height to the hypotenuse.

Answer 1

Please see the attached picture to see the similar triangle.  

The new triangle has triple the side lengths of the first one.  This means all side lengths will be triple.

You will use this ratio to find the new side lengths and then use them to find the perimeter and area.

3:4:5 = 9 cm: 12 cm:15 cm on triangleABC

1.  The perimeter is 9cm + 12 cm + 15 cm or 36 cm.

2.  The area is 1/2 x 12 x 9 or 54 square cm.

3.  The length of the hypotenuse is 15 cm.