Question

the glass door is made of 150 triangle and 75 rectangle the area of each triangle is half of the area of each rectangle. if total area of glass used to make the glass door is 3600sq.cm and common side of rectangle and triangle is 4 cm find the length of each rectangle and height of each triangle

Answer 1

the answer is 6, is it okay?

Answer 2

Answer:

Length of the rectangle = Height of the triangle = 6 cm.

Step-by-step explanation:

We are given that, the glass door is made up of 150 triangles and 75 rectangles.

Also, 'area of a triangle is half of the area of a rectangle'.

i.e. $A_{T}=\frac{1}{2}\times A_{R}$

As, the total area of the glass door = 3600 sq. cm

We get the equation,

$150A_{T}+75A_{R}=3600$

i.e. $150(\frac{1}{2}\times A_{R})+75A_{R}=3600$

i.e. $75A_{R}+75A_{R}=3600$

i.e. $150A_{R}=3600$

i.e. $A_{R}=24$ sq.cm

Then, $A_{T}=\frac{1}{2}\times A_{R}$

i.e. $A_{T}=\frac{1}{2}\times 24$

$A_{T}=12$ sq.cm

Now, we have that,

Dimension of the common side of the rectangle and triangle = 4 cm.

So, we get, Area of rectangle = Length × Width

i.e. 24 = Length × 4

i.e. Length = 6 cm

Hence, length of the rectangle = 6 cm.

Also, Area of the triangle = $\frac{1}{2}\times Base\times Height$

i.e. Area of the triangle = $\frac{1}{2}\times 4\times Height$

i.e. 12 = $2\times Height$

i.e. Height = 6 cm.

Hence, height of the triangle = 6 cm.

Therefore, length of the rectangle and height of the triangle is 6 cm.