Answer and Step-by-step explanation: Area of a right triangle, (as any other triangle), is calculated as:
Area of a rectangle is calculated as:
Area of a right trapezoid is: , where:
a is short base
b is long base
h is height
1) Expressing areas in terms of x:
Area of triangle S1:
Area of rectangle S2:
Area of trapezoid S3:
2) a)
Which is the same as S = (2x-3)(5x-9)
b) For the areas to be the same:
Using Bhaskara to solve the second degree equation:
= 1.8
= 1.5
For the areas of AFGC and ADEB to be equal, x has to be 1.5 or 1.8.
c) <u>Expand</u> <u>a</u> <u>polynomial</u> (or equation) is to multiply all the terms, remiving the parenthesis. <u>Reduce</u> <u>a</u> <u>polynomial</u> (or equation) is to combine terms alike,e.g.:
(expand)
(reduce)
d) For area of AFCG to be bigger than area of ADEB by 27:
Solving:
2.82
= 0.48
According to the enunciation, x cannot be less than 1.5, then, the value of x so that area AFGC exceeds the area ADEB by 27 is 2.82