Express the area of the triangle ABC in terms of X. 2X 2X 2X A A A B B B C C C D D D 8 X+1

$$ \frac{X+9}{2}\sqrt{5X^2+2X+1} $$

Using the Pythagorean Theorem: Using variables

The Perimeter of a Triangle Two triangles Applying the formula In combination with the triangle area Isosceles triangle Mathematical space and motion problems Reverse use of theorem Using ratios for calculation Calculation using the diagonal Using Pythagoras' theorem Using additional geometric shapes

Question 1

The triangle in the figure is isosceles.

The length of the hypotenuse is $\frac{x+3}{\sqrt{2}}$ cm.

Work out the length of the leg.

Question 2

Look at the triangles in the figure.

Express the length DB in terms of X.

Question 3

Look at the triangle in the figure.

$$ a+b=7 $$

The ratio between CB and AC is 5:3.

Calculate: $$ a,b $$ .

Question 4

Look at the triangle in the diagram below.

Is it a right triangle?

Question 5

Express the area of the triangle ABC in terms of X.

Examples with solutions for Using the Pythagorean Theorem: Using variables

Exercise #1

The triangle in the figure is isosceles.

The length of the hypotenuse is $\frac{x+3}{\sqrt{2}}$ cm.

Work out the length of the leg.

Video Solution

Answer

$\frac{x+3}{2}$ cm

Exercise #2

Look at the triangles in the figure.

Express the length DB in terms of X.

Video Solution

Answer

$\sqrt{32+x^2}$ cm

Exercise #3

Look at the triangle in the figure.

$a+b=7$

The ratio between CB and AC is 5:3.

Calculate: $a,b$ .

Video Solution

Answer

$a=3\text{ }b=4$

Exercise #4

Look at the triangle in the diagram below.

Is it a right triangle?

Video Solution

Answer

No, the angle is obtuse.

Exercise #5

Express the area of the triangle ABC in terms of X.

Video Solution

Answer

$\frac{X+9}{2}\sqrt{3X^2-2X-1}$