Name: Trigonometric Ratios for the Angle of 30 Degrees
Uploaded: 2019-07-19
Duration: 3 min 17 s
Description: What is the angular bisector of 60 degrees? It is 30 degree. Wondering how? Let us learn the trigonometric ratios of 30 degree in this interesting video!

Question

George has a right-angled isosceles triangle and Prita has a similar triangle which has a hypotenuse of $\sqrt{800} c m$ . The area of prita's triangle is four times the area of George's triangle. Find the dimensions of George's triangle.

Accepted Answer

George has a right-angled isosceles triangle and Prita has a similar triangle which has a hypotenuse of $= \sqrt{800} c m$ .

The area of Prita's triangle is four times the area of George's triangle.

The ratio of the areas of two similar triangles is equal to the square of the ratio of any pair of their corresponding sides.

$\Rightarrow$ Area of Prita's triangle $/$ Area of George's triangle $= {(\frac{S i d e o f P r i t a' s t r i a n g l e}{S i d e o f G e o r g e' s t r i a n g l e})}^{2}$

$\Rightarrow \frac{{(\sqrt{800})}^{2}}{x^{2}} = \frac{4}{1} \Rightarrow x^{2} = \frac{800}{4} = 200 \Rightarrow x = \sqrt{200}$

We have to find the dimensions of George's triangle.

Hypotenuse of George's triangle $= \sqrt{200} c m$

The base of the triangle is equal to the length of the perpendicular $= x$

The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

$\Rightarrow {(\sqrt{200})}^{2} = x^{2} + x^{2} \Rightarrow 2 x^{2} = 200 \Rightarrow x^{2} = \frac{200}{2} = 100 \Rightarrow x = \sqrt{100} = 10 c m$

Hence, length of the sides of triangle are $10 c m, 10 c m, \sqrt{200} c m$ .

George has a right-angled isosceles triangle and Prita has a similar triangle which has a hypotenuse of $\sqrt{800} c m$ . The area of prita's triangle is four times the area of George's triangle. Find the dimensions of George's triangle.

Important Questions on Triangles Principles, Processes and Solutions

Learn and Prepare for any exam you want !

George has a right-angled isosceles triangle and Prita has a similar triangle which has a hypotenuse of 800 cm. The area of prita's triangle is four times the area of George's triangle. Find the dimensions of George's triangle.

Important Questions on Triangles Principles, Processes and Solutions

Learn and Prepare for any exam you want !

George has a right-angled isosceles triangle and Prita has a similar triangle which has a hypotenuse of $\sqrt{800} c m$ . The area of prita's triangle is four times the area of George's triangle. Find the dimensions of George's triangle.