The expression described is translated into the following formula:
Note that this implies that
Cross-multiply denominators to get rid of the fractions:
Expand both sides:
Subtract 4x from both sides:
Divide both sides by 2:
Check:
Which is true because
since both sides evaluate to 72
Area of a triangle = (1/2)*base*height
For both of the triangles, you have the base (8.8 for the triangle on the left, 7.6 for the triangle on the right) and the side lengths, but not the height. But since both are isosceles triangles, you can find the height using the pythagorean theorem.
5.
First divide the triangle vertically into two triangles (see attached picture). Now you have two right triangles, you can apply the pythagorean theorem on either one of them to find the height. The pythagorean theorem says that for a right triangle, , where c is the hypotenuse and a and b are the sides of the triangle.
Substituting the given values and rounding to nearest tenth:
Now that you have the height, you can find the area of the entire triangle.
A = (1/2)*base*height
A = (1/2)*8.8*9.0 = 39.6
6.
Same procedure.
A = (1/2)*base*height
A = (1/2)*7.6*9.2 = 35.0
