Question

The diagram shows a rectangle split into three triangles. The total shaded area is 8.5cm². Work out the value of x. Give your answer to 1 decimal place.

Answer 1

Based on the diagram showing a rectangle split into three triangles, the value of x is 1.5 cm.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):

Area of triangle = 1/2 × b × h

Where:

• b represent the base area.
• h represent the height.

In order to determine the value of x, we would set up an equation as follows;

Total shaded area = 1/2 × base × height

8.5 = 1/2 × (3x + 1) × 2x

`8.5 = 3x^2+x\\\\3x^2+x-8.5=0\\\\x = (-b\; \pm \;√(b^2 - 4ac))/(2a)\\\\x = (-1\; \pm \;√(1^2 - 4(3)(-8.5)))/(2(3))\\\\x = (-1\; \pm \;√(1 +102))/(6)\\\\x = (-1\; \pm \;√(103))/(6)\\\\x = (-1\; \pm \;10.1489)/(6)`

x = (-1 - 10.1489)/6

x = -1.9

x = (-1 + 10.1489)/6

x = 1.5.

Since the dimensions of any geometric shape must be positive, the value of x is 1.5 cm.

Complete Question:

The diagram shows a rectangle split into three triangles. The total shaded area is 8.5cm². Work out the value of x. Give your answer to 1 decimal place.