Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.
Answers
Answer:
hope it would be of great help
To draw the similar triangle with 3/4th the measure of each side, we use the Pythagorean theorem to find the third sides of both triangles.
Explanation:
We have the measure of two sides of the first triangle.
So we have to find the measure of the third side, which is the Hypotenuse of the triangle.
If ABC is the first triangle, right angled at B, then AB = 8 cm, BC = 6 cm. CA = ?
Using Pythagoras theorem, we get
AB^2 + BC^2 = AC^2
AC^2 = AB^2 + BC^2.
AC^2 = 8^2 + 6^2
AC^2 = 64 + 36
AC^2 = 100
Or, AC = √100 = 10 cm.
Now, for second triangle PQR which is right angled at Q, we find the length of two sides first.
Each side is ¾ of first triangle, so we calculate ¾ of each side.
¾ of AB = ¾ of 8 cm = 6cm.
¾ of BC = ¾ of 6 cm = 4.5 cm.
¾ of CA =3/4 of 10 cm = 7.5 cm.
So the second triangle PQR will have following measure of sides:-
PQ = 6 cm.
QR = 4.5 cm.
PR = 7.5 cm. (right angled at Q).
(Figure attached).
