area of triangle - One side of a right angle triangle is twice the other, and the hypotenuse is 10 cm. The area of the triangle is___

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: According to the given hints, say a variable

EXAMPLE: Let "x" be the length of one side

length of other side = 2x

Step 2: Find the sides of the right triangle using the Pythagoras theorem.

EXAMPLE: Pythagoras formula = (Hypotenuse)^2 = side^2 + side^2

10^2 = x^2 + (2x)^2

100 = 5x^2

x = 2 \sqrt{5} cm

Step 3: Substitute x value in the length of the other side

EXAMPLE 2x = 2*2\sqrt{5} cm

= 4 \sqrt{5}

Step 4: Find the area of the of the right triangle

NOTE: In right triangle

One side = altitude

Another side = base

EXAMPLE: Area of the triangle = \frac{1}{2} base * altitude

= \frac{1}{2} (2 \sqrt{5}) * (4 \sqrt{5})

= 20 square cm