Question

The rectangles are congruent, each with area 9. What’s the area of the triangle?​

Answer 1

Given :  The rectangles are congruent, each with area 9

To find : Area of Triangle

Solution:

Let say Side of rectangle are L & B

Area of Triangle = (1/2) (L - B)  (L + B)    ( (1/2) Base * height )

= (1/2) (L² - B²)

Now if we see two Triangles

one on the base of left side and another  right side of right rectangle

these are similar triangle as sides of rectangle are parallel

then B/(L - B)  =  √(L² + L²) / √((L + B)² + (L + B)²)

=> B/(L - B) = L√2 / (L + B)√2

=>  B/(L - B) = L/(L + B)

=> BL + B² = L² - LB

=> L² - B² = 2LB

Area of Triangle =  (1/2) (L² - B²)

= (1/2) 2LB

= LB

LB  = Area of rectangle = 9

=> Area of Triangle =  9

Learn More:

You have one room of 12 ft x 12 ft.

https://brainly.in/question/16833687

Find the area of rectangle

https://brainly.in/question/16639271