Confused with this triangle area problem?
"The sum of the area of two triangles is 120cm^2. The triangles overlap to create another triangle, which is shaded. If 2/3 of the smaller triangle is unshaded, and 8/9 of the larger triangle is unshaded, what is the area of the shaded overlapping triangle?"
I tried to set up a system relating the two, but had two variables in one, and three in the other. Substitution only proved x = x for me. :p
Could someone get me started on the right path?
The part that is overlapping (shaded) is 1/3 of the smaller triangle, and 1/9 of the larger triangle.
S = area of the smaller triangle
L = area of the larger triangle
(1/3)S = (1/9)L
S = (1/3)L
You know that S + L = 120
By substitution, (1/3)L + L = 120
(4/3)L = 120
L = 90
S = 30
(1/3) of 30 = 10
(1/9) of 90 = 10
The overlapping area is 10cm²
The part that is overlapping (shaded) is 1/3 of the smaller triangle, and 1/9 of the larger triangle.
S = area of the smaller triangle
L = area of the larger triangle
(1/3)S = (1/9)L
S = (1/3)L
You know that S + L = 120
By substitution, (1/3)L + L = 120
(4/3)L = 120
L = 90
S = 30
(1/3) of 30 = 10
(1/9) of 90 = 10
The overlapping area is 10cm²
References :
I teach high school algebra